diff --git a/src/Data/Profunctor/Kleisli/Linear.hs b/src/Data/Profunctor/Kleisli/Linear.hs
index 69ba3794..70539d6e 100644
--- a/src/Data/Profunctor/Kleisli/Linear.hs
+++ b/src/Data/Profunctor/Kleisli/Linear.hs
@@ -43,6 +43,10 @@ instance Control.Applicative f => Strong Either Void (Kleisli f) where
   first  (Kleisli f) = Kleisli (either (Data.fmap Left . f) (Control.pure . Right))
   second (Kleisli g) = Kleisli (either (Control.pure . Left) (Data.fmap Right . g))
 
+instance Control.Applicative f => Monoidal (,) () (Kleisli f) where
+  Kleisli f *** Kleisli g = Kleisli $ \(x,y) -> (,) Control.<$> f x Control.<*> g y
+  unit = Kleisli Control.pure
+
 instance Control.Applicative f => Wandering (Kleisli f) where
   wander (Kleisli f) = Kleisli (Data.traverse f)
 
diff --git a/src/Data/Profunctor/Linear.hs b/src/Data/Profunctor/Linear.hs
index ca924896..b2fff9f1 100644
--- a/src/Data/Profunctor/Linear.hs
+++ b/src/Data/Profunctor/Linear.hs
@@ -80,6 +80,10 @@ instance Strong Either Void LinearArrow where
   first  (LA f) = LA $ either (Left . f) Right
   second (LA g) = LA $ either Left (Right . g)
 
+instance Monoidal (,) () LinearArrow where
+  LA f *** LA g = LA $ \(a,x) -> (f a, g x)
+  unit = LA id
+
 instance Profunctor (->) where
   dimap f g h x = g (h (f x))
 instance Strong (,) () (->) where
@@ -87,6 +91,9 @@ instance Strong (,) () (->) where
 instance Strong Either Void (->) where
   first f (Left x) = Left (f x)
   first _ (Right y) = Right y
+instance Monoidal (,) () (->) where
+  (f *** g) (a,x) = (f a, g x)
+  unit () = ()
 
 data Exchange a b s t = Exchange (s #-> a) (b #-> t)
 instance Profunctor (Exchange a b) where
@@ -104,6 +111,10 @@ instance Prelude.Applicative f => Strong Either Void (Kleisli f) where
                                    Left  x -> Prelude.fmap Left (f x)
                                    Right y -> Prelude.pure (Right y)
 
+instance Prelude.Applicative f => Monoidal (,) () (Kleisli f) where
+  Kleisli f *** Kleisli g = Kleisli (\(x,y) -> (,) Prelude.<$> f x Prelude.<*> g y)
+  unit = Kleisli Prelude.pure
+
 data Market a b s t = Market (b #-> t) (s #-> Either t a)
 runMarket :: Market a b s t #-> (b #-> t, s #-> Either t a)
 runMarket (Market f g) = (f, g)