diff --git a/src/stim/dem/detector_error_model.cc b/src/stim/dem/detector_error_model.cc
index 6f663dbf..c2282faa 100644
--- a/src/stim/dem/detector_error_model.cc
+++ b/src/stim/dem/detector_error_model.cc
@@ -16,6 +16,7 @@
 
 #include "stim/dem/detector_error_model.h"
 
+#include <algorithm>
 #include <cmath>
 #include <iomanip>
 #include <limits>
@@ -793,3 +794,86 @@ DetectorErrorModel DetectorErrorModel::without_tags() const {
     }
     return result;
 }
+
+bool is_structural(DemInstructionType type) {
+    return type == DemInstructionType::DEM_SHIFT_DETECTORS || type == DemInstructionType::DEM_REPEAT_BLOCK;
+}
+
+bool is_equal_up_to_instruction_ordering_helper(const DetectorErrorModel &a, const DetectorErrorModel &b) {
+    size_t index_in_a = 0;
+    size_t index_in_b = 0;
+
+    auto get_next_segment = [](const DetectorErrorModel &dem, size_t &i) {
+        std::vector<DemInstruction> segment;
+        while (i < dem.instructions.size() && !is_structural(dem.instructions[i].type)) {
+            segment.push_back(dem.instructions[i]);
+            i++;
+        }
+        std::sort(segment.begin(), segment.end());
+        return segment;
+    };
+
+    while (true) {
+        // compare next segments
+        auto segment_a = get_next_segment(a, index_in_a);
+        auto segment_b = get_next_segment(b, index_in_b);
+        if (segment_a != segment_b) {
+            return false;
+        }
+
+        // check for terminating condition
+        bool traversed_a = index_in_a == a.instructions.size();
+        bool traversed_b = index_in_b == b.instructions.size();
+        if (traversed_a || traversed_b) {
+            return traversed_a && traversed_b;
+        }
+
+        // compare next structural ops
+        const auto &structural_op_a = a.instructions[index_in_a];
+        const auto &structural_op_b = b.instructions[index_in_b];
+
+        if (structural_op_a.type != structural_op_b.type) {
+            return false;
+        }
+
+        if (structural_op_a.tag != structural_op_b.tag) {
+            return false;
+        }
+
+        if (structural_op_a.type == DemInstructionType::DEM_SHIFT_DETECTORS) {
+            // check coordinate shift
+            if (structural_op_a.arg_data != structural_op_b.arg_data) {
+                return false;
+            }
+            // check index shift
+            if (structural_op_a.target_data[0].data != structural_op_b.target_data[0].data) {
+                return false;
+            }
+            // advance to next op
+            index_in_a++;
+            index_in_b++;
+            continue;
+        }
+
+        if (structural_op_a.type == DemInstructionType::DEM_REPEAT_BLOCK) {
+            // check reps
+            if (structural_op_a.repeat_block_rep_count() != structural_op_b.repeat_block_rep_count()) {
+                return false;
+            }
+            // check equality of repeat body
+            const auto &body_a = structural_op_a.repeat_block_body(a);
+            const auto &body_b = structural_op_b.repeat_block_body(b);
+            if (!is_equal_up_to_instruction_ordering_helper(body_a, body_b)) {
+                return false;
+            }
+            // advance to next op
+            index_in_a++;
+            index_in_b++;
+            continue;
+        }
+    }
+}
+
+bool DetectorErrorModel::is_equal_up_to_instruction_ordering(const DetectorErrorModel &other) const {
+    return is_equal_up_to_instruction_ordering_helper(*this, other);
+}
diff --git a/src/stim/dem/detector_error_model.h b/src/stim/dem/detector_error_model.h
index 0f5d53d5..68bbe6ed 100644
--- a/src/stim/dem/detector_error_model.h
+++ b/src/stim/dem/detector_error_model.h
@@ -135,6 +135,14 @@ struct DetectorErrorModel {
 
     /// Returns an equivalent detector error model with no repeat blocks or detector_shift instructions.
     DetectorErrorModel flattened() const;
+
+    /// Returns true if the detector error model is equal to the other detector error model up to instruction ordering,
+    /// within segments between structural instructions. Structural instructions (`shift_detectors` and `repeat`) must
+    /// match exactly and in the same order, and `repeat` bodies are compared recursively. Within each segment,
+    /// `error`/`detector`/`logical_observable` instructions are compared order-insensitively.
+    ///
+    /// Note: worst-case time is O(n log n) due to sorting segments.
+    bool is_equal_up_to_instruction_ordering(const DetectorErrorModel &other) const;
 };
 
 void print_detector_error_model(std::ostream &out, const DetectorErrorModel &v, size_t indent);
diff --git a/src/stim/dem/detector_error_model.test.cc b/src/stim/dem/detector_error_model.test.cc
index 429642c9..e53c05a5 100644
--- a/src/stim/dem/detector_error_model.test.cc
+++ b/src/stim/dem/detector_error_model.test.cc
@@ -894,3 +894,232 @@ TEST(detector_error_model, parse_windows_newlines) {
         DetectorErrorModel("error(0.125) D0\r\ndetector(5) D10\r\n"),
         DetectorErrorModel("error(0.125) D0\r\ndetector(5) D10\r\n"));
 }
+
+/// Without structural barriers, a segment compares as an order-insensitive instruction sequence.
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_flattened) {
+    DetectorErrorModel lhs(R"MODEL(
+        error[dead](0.01) D0
+        error(0.002) D1 L0
+        detector(5, 10) D0
+        detector(5, 15) D1
+        logical_observable L0
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        error(0.002) D1 L0
+        error[dead](0.01) D0
+        detector(5, 15) D1
+        detector(5, 10) D0
+        logical_observable L0
+    )MODEL");
+    EXPECT_TRUE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}
+
+/// Segment comparison includes tags, so a mismatched tag causes inequality.
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_flattened_tag_mismatch) {
+    DetectorErrorModel lhs(R"MODEL(
+        error[dead](0.01) D0
+        error(0.002) D1 L0
+        detector(5, 10) D0
+        detector(5, 15) D1
+        logical_observable L0
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        error(0.002) D1 L0
+        error[beef](0.01) D0
+        detector(5, 15) D1
+        detector(5, 10) D0
+        logical_observable L0
+    )MODEL");
+    EXPECT_FALSE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}
+
+/// An extra `shift_detectors` barrier (even shifting by 0) makes models not equal.
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_shift_missing) {
+    DetectorErrorModel lhs(R"MODEL(
+        error(0.1) D0
+        shift_detectors 0
+        error(0.2) D1
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        error(0.1) D0
+        error(0.2) D1
+    )MODEL");
+    EXPECT_FALSE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}
+
+/// `shift_detectors(...)` barriers must match exactly (including the coordinate shift vector).
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_shift_mismatch) {
+    DetectorErrorModel lhs(R"MODEL(
+        detector(5, 10) D0
+        detector(5, 15) D1
+        shift_detectors(0, 1) 1
+        detector(5, 10) D0
+        detector(5, 15) D1
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        detector(5, 10) D0
+        detector(5, 15) D1
+        shift_detectors(1, 1) 1
+        detector(5, 15) D1
+        detector(5, 10) D0
+    )MODEL");
+    EXPECT_FALSE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}
+
+/// `shift_detectors` barriers must match exactly (including tags).
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_shift_tag_mismatch) {
+    DetectorErrorModel lhs(R"MODEL(
+        detector(5, 10) D0
+        detector(5, 15) D1
+        shift_detectors[dead](0, 1) 1
+        detector(5, 10) D0
+        detector(5, 15) D1
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        detector(5, 10) D0
+        detector(5, 15) D1
+        shift_detectors[beef](0, 1) 1
+        detector(5, 15) D1
+        detector(5, 10) D0
+    )MODEL");
+    EXPECT_FALSE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}
+
+/// Segment order-insensitivity is allowed on either side of a matching `shift_detectors` barrier.
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_shift_once) {
+    DetectorErrorModel lhs(R"MODEL(
+        detector(5, 10) D0
+        detector(5, 15) D1
+        shift_detectors[dead](0, 1) 1
+        detector(5, 10) D0
+        detector(5, 15) D1
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        detector(5, 10) D0
+        detector(5, 15) D1
+        shift_detectors[dead](0, 1) 1
+        detector(5, 15) D1
+        detector(5, 10) D0
+    )MODEL");
+    EXPECT_TRUE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}
+
+/// Multiple `shift_detectors` barriers create multiple independently order-insensitive segments.
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_shift_twice) {
+    DetectorErrorModel lhs(R"MODEL(
+        detector(5, 10) D0
+        detector(5, 15) D1
+        shift_detectors[dead](0, 1) 1
+        detector(5, 10) D0
+        detector(5, 15) D1
+        shift_detectors 1
+        error(0.01) D0
+        error(0.002) D1 L0
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        detector(5, 10) D0
+        detector(5, 15) D1
+        shift_detectors[dead](0, 1) 1
+        detector(5, 15) D1
+        detector(5, 10) D0
+        shift_detectors 1
+        error(0.002) D1 L0
+        error(0.01) D0
+    )MODEL");
+    EXPECT_TRUE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}
+
+/// `repeat` blocks are structural barriers and must match on repetition count.
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_repeat_reps_mismatch) {
+    DetectorErrorModel lhs(R"MODEL(
+        repeat 3 {
+            error(0.002) D1 L0
+            error(0.01) D0
+            shift_detectors 1
+        }
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        repeat 2 {
+            error(0.002) D1 L0
+            error(0.01) D0
+            shift_detectors 1
+        }
+    )MODEL");
+    EXPECT_FALSE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}
+
+/// Identical `repeat` blocks compare equal without unrolling.
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_repeat) {
+    DetectorErrorModel lhs(R"MODEL(
+        repeat 3 {
+            error(0.002) D1 L0
+            error(0.01) D0
+            shift_detectors 1
+        }
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        repeat 3 {
+            error(0.002) D1 L0
+            error(0.01) D0
+            shift_detectors 1
+        }
+    )MODEL");
+    EXPECT_TRUE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}
+
+/// A `repeat` block is not equal to an unrolled equivalent (barrier alignment is required).
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_repeat_versus_inline) {
+    DetectorErrorModel lhs(R"MODEL(
+        repeat 2 {
+            error(0.1) D0
+            shift_detectors 1
+        }
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        error(0.1) D0
+        shift_detectors 1
+        error(0.1) D0
+        shift_detectors 1
+    )MODEL");
+    EXPECT_FALSE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}
+
+/// Empty segments between consecutive structural barriers are handled correctly.
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_consecutive_barriers_ok) {
+    DetectorErrorModel lhs(R"MODEL(
+        shift_detectors 1
+        shift_detectors 2
+        error(0.1) D0
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        shift_detectors 1
+        shift_detectors 2
+        error(0.1) D0
+    )MODEL");
+    EXPECT_TRUE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}
+
+/// Nested `repeat` blocks compare recursively, allowing order-insensitive segments inside the inner body.
+TEST(detector_error_model, is_equal_up_to_instruction_ordering_nested_repeats) {
+    DetectorErrorModel lhs(R"MODEL(
+        repeat 2 {
+            repeat 3 {
+                error(0.1) D0
+                error(0.2) D1
+                shift_detectors 1
+            }
+            shift_detectors 5
+        }
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        repeat 2 {
+            repeat 3 {
+                error(0.2) D1
+                error(0.1) D0
+                shift_detectors 1
+            }
+            shift_detectors 5
+        }
+    )MODEL");
+    EXPECT_TRUE(lhs.is_equal_up_to_instruction_ordering(rhs));
+}