diff --git a/benchmark/Streamly/Benchmark/Prelude/Serial/NestedStream.hs b/benchmark/Streamly/Benchmark/Prelude/Serial/NestedStream.hs
index c6fe765b95..4c496320d7 100644
--- a/benchmark/Streamly/Benchmark/Prelude/Serial/NestedStream.hs
+++ b/benchmark/Streamly/Benchmark/Prelude/Serial/NestedStream.hs
@@ -461,6 +461,11 @@ o_n_heap_buffering value =
             $ joinWith Internal.intersectBy sqrtVal
         , benchIOSrc1 "intersectBySorted"
             $ joinMapWith (Internal.intersectBySorted compare) halfVal
+        -- XXX It hangs forever
+        --, benchIOSrc1 "differenceBy"
+        --    $ joinMapWith (Internal.differenceBy (==)) halfVal
+        , benchIOSrc1 "differenceBySorted"
+            $ joinMapWith (Internal.differenceBySorted compare) sqrtVal
         ]
     ]
 
diff --git a/core/src/Streamly/Internal/Data/Stream/StreamD/Nesting.hs b/core/src/Streamly/Internal/Data/Stream/StreamD/Nesting.hs
index 821ccb97bd..6fecb60011 100644
--- a/core/src/Streamly/Internal/Data/Stream/StreamD/Nesting.hs
+++ b/core/src/Streamly/Internal/Data/Stream/StreamD/Nesting.hs
@@ -143,6 +143,7 @@ module Streamly.Internal.Data.Stream.StreamD.Nesting
     , splitInnerBy
     , splitInnerBySuffix
     , intersectBySorted
+    , differenceBySorted
     )
 where
 
@@ -487,6 +488,25 @@ mergeBy cmp = mergeByM (\a b -> return $ cmp a b)
 -- Intersection of sorted streams
 -------------------------------------------------------------------------------
 
+data StreamEmptyNess =
+      LeftEmpty
+    | RightEmpty
+    | BothEmpty
+    | NoneEmpty
+        deriving (Eq, Show)
+
+data RunOrder =
+      LeftRun
+    | RightRun
+    | CompareRun
+    | CompareDupRun
+    | FastFarwardRun
+    | RightDupRun
+    | BuffPrepare
+    | BuffPair
+    | BuffReset
+        deriving (Eq, Show)
+
 -- Assuming the streams are sorted in ascending order
 {-# INLINE_NORMAL intersectBySorted #-}
 intersectBySorted :: Monad m
@@ -2466,3 +2486,67 @@ splitInnerBySuffix splitter joiner (Stream step1 state1) =
 
     step _ (SplitYielding x next) = return $ Yield x next
     step _ SplitFinishing = return Stop
+
+-------------------------------------------------------------------------------
+-- Difference of sorted streams -----------------------------------------------
+-------------------------------------------------------------------------------
+{-# INLINE_NORMAL differenceBySorted #-}
+differenceBySorted :: (Monad m) =>
+    (a -> a -> Ordering) -> Stream m a -> Stream m a -> Stream m a
+differenceBySorted cmp (Stream stepa ta) (Stream stepb tb) =
+    Stream step (Just ta, Just tb, Nothing, Nothing, Nothing)
+
+    where
+    {-# INLINE_LATE step #-}
+
+    -- one of the values is missing, and the corresponding stream is running
+    step gst (Just sa, sb, Nothing, b, Nothing) = do
+        r <- stepa gst sa
+        return $ case r of
+            Yield a sa' -> Skip (Just sa', sb, Just a, b, Nothing)
+            Skip sa'    -> Skip (Just sa', sb, Nothing, b, Nothing)
+            Stop        -> Skip (Nothing, sb, Nothing, b, Nothing)
+
+    step gst (sa, Just sb, a, Nothing, Nothing) = do
+        r <- stepb gst sb
+        return $ case r of
+            Yield b sb' -> Skip (sa, Just sb', a, Just b, Nothing)
+            Skip sb'    -> Skip (sa, Just sb', a, Nothing, Nothing)
+            Stop        -> Skip (sa, Nothing, a, Nothing, Nothing)
+
+    -- Matching element
+    step gst (Just sa, Just sb, Nothing, _, Just _) = do
+        r1 <- stepa gst sa
+        r2 <- stepb gst sb
+        return $ case r1 of
+            Yield a sa' ->
+                case r2 of
+                    Yield c sb' ->
+                        Skip (Just sa', Just sb', Just a, Just c, Nothing)
+                    Skip sb' ->
+                        Skip (Just sa', Just sb', Just a, Just a, Nothing)
+                    Stop ->
+                        Yield a (Just sa', Just sb, Nothing, Nothing, Just a)
+            Skip sa' ->
+                case r2 of
+                    Yield c sb' ->
+                        Skip (Just sa', Just sb', Just c, Just c, Nothing)
+                    Skip sb' ->
+                        Skip (Just sa', Just sb', Nothing, Nothing, Nothing)
+                    Stop ->
+                        Stop
+            Stop ->
+                Stop
+
+    -- both the values are available
+    step _ (sa, sb, Just a, Just b, Nothing) = do
+        let res = cmp a b
+        return $ case res of
+            GT -> Skip (sa, sb, Just a, Nothing, Nothing)
+            LT -> Yield a (sa, sb, Nothing, Just b, Nothing)
+            EQ -> Skip (sa, sb, Nothing, Just b, Just b)
+
+    -- one of the values is missing, corresponding stream is done
+    step _ (sa, Nothing, Just a, Nothing, Nothing) =
+        return $ Yield a (sa, Nothing, Nothing, Nothing , Nothing)
+    step _ (_, _, _, _, _) = return Stop
diff --git a/src/Streamly/Internal/Data/Stream/IsStream/Top.hs b/src/Streamly/Internal/Data/Stream/IsStream/Top.hs
index b6992e5c5c..1021d215e8 100644
--- a/src/Streamly/Internal/Data/Stream/IsStream/Top.hs
+++ b/src/Streamly/Internal/Data/Stream/IsStream/Top.hs
@@ -30,7 +30,7 @@ module Streamly.Internal.Data.Stream.IsStream.Top
     , intersectBy
     , intersectBySorted
     , differenceBy
-    , mergeDifferenceBy
+    , differenceBySorted
     , unionBy
     , mergeUnionBy
 
@@ -632,11 +632,14 @@ differenceBy eq s1 s2 =
 --
 -- Space: O(1)
 --
--- /Unimplemented/
-{-# INLINE mergeDifferenceBy #-}
-mergeDifferenceBy :: -- (IsStream t, Monad m) =>
+-- /Pre-release/
+{-# INLINE differenceBySorted #-}
+differenceBySorted :: (IsStream t, MonadIO m) =>
     (a -> a -> Ordering) -> t m a -> t m a -> t m a
-mergeDifferenceBy _eq _s1 _s2 = undefined
+differenceBySorted eq s1 =
+      IsStream.fromStreamD
+    . StreamD.differenceBySorted eq (IsStream.toStreamD s1)
+    . IsStream.toStreamD
 
 -- | This is essentially an append operation that appends all the extra
 -- occurrences of elements from the second stream that are not already present
diff --git a/test/Streamly/Test/Prelude/Top.hs b/test/Streamly/Test/Prelude/Top.hs
index 84f814d81d..a2b0866144 100644
--- a/test/Streamly/Test/Prelude/Top.hs
+++ b/test/Streamly/Test/Prelude/Top.hs
@@ -1,6 +1,6 @@
 module Main (main) where
 
-import Data.List (elem, intersect, nub, sort)
+import Data.List (elem, intersect, nub, sort, (\\))
 import Data.Maybe (isNothing)
 import Streamly.Prelude (SerialT)
 import Test.QuickCheck
@@ -196,6 +196,25 @@ intersectBy srt intersectFunc cmp =
                 let v2 = ls0 `intersect` ls1
                 assert (sort v1 == sort v2)
 
+differenceBySorted :: Property
+differenceBySorted =
+    forAll (listOf (chooseInt (min_value, max_value))) $ \ls0 ->
+        forAll (listOf (chooseInt (min_value, max_value))) $ \ls1 ->
+            monadicIO $ action (sort ls0) (sort ls1)
+
+            where
+
+            action ls0 ls1 = do
+                v1 <-
+                    run
+                    $ S.toList
+                    $ Top.differenceBySorted
+                        compare
+                        (S.fromList ls0)
+                        (S.fromList ls1)
+                let v2 = ls0 \\ ls1
+                assert (v1 == sort v2)
+
 -------------------------------------------------------------------------------
 -- Main
 -------------------------------------------------------------------------------
@@ -219,3 +238,4 @@ main = hspec $ do
             (intersectBy id Top.intersectBy (==))
         prop "intersectBySorted"
             (intersectBy sort Top.intersectBySorted compare)
+        prop "differenceBySorted" Main.differenceBySorted