diff --git a/changelog.md b/changelog.md
--- a/changelog.md
+++ b/changelog.md
@@ -1,3 +1,6 @@
+0.7.5.0
+* Add Semigroup instance when the Semigroup class is available through base.
+
 0.7.4.3
 * Loosen dependency upper bounds.
 
diff --git a/retry.cabal b/retry.cabal
--- a/retry.cabal
+++ b/retry.cabal
@@ -14,7 +14,7 @@
         case we should hang back for a bit and retry the query instead
         of simply raising an exception.
 
-version:             0.7.4.3
+version:             0.7.5.0
 synopsis:            Retry combinators for monadic actions that may fail
 license:             BSD3
 license-file:        LICENSE
diff --git a/src/Control/Retry.hs b/src/Control/Retry.hs
--- a/src/Control/Retry.hs
+++ b/src/Control/Retry.hs
@@ -94,7 +94,11 @@
 import           GHC.Prim
 import           GHC.Types (Int(I#))
 import           System.Random
+# if MIN_VERSION_base(4, 9, 0)
+import           Data.Semigroup
+# else
 import           Data.Monoid
+# endif
 import           Prelude                hiding (catch)
 -------------------------------------------------------------------------------
 
@@ -149,12 +153,28 @@
     def = constantDelay 50000 <> limitRetries 5
 
 
+-- Base 4.9.0 adds a Data.Semigroup module. This has fewer
+-- dependencies than the semigroups package, so we're using base's
+-- only if its available.
+# if MIN_VERSION_base(4, 9, 0)
+instance Monad m => Semigroup (RetryPolicyM m) where
+  (RetryPolicyM a) <> (RetryPolicyM b) = RetryPolicyM $ \ n -> runMaybeT $ do
+    a' <- MaybeT $ a n
+    b' <- MaybeT $ b n
+    return $! max a' b'
+
+
 instance Monad m => Monoid (RetryPolicyM m) where
     mempty = retryPolicy $ const (Just 0)
+    mappend = (<>)
+# else
+instance Monad m => Monoid (RetryPolicyM m) where
+    mempty = retryPolicy $ const (Just 0)
     (RetryPolicyM a) `mappend` (RetryPolicyM b) = RetryPolicyM $ \ n -> runMaybeT $ do
       a' <- MaybeT $ a n
       b' <- MaybeT $ b n
       return $! max a' b'
+#endif
 
 
 -------------------------------------------------------------------------------