diff --git a/core/src/main/scala/cats/functor/Bifunctor.scala b/core/src/main/scala/cats/functor/Bifunctor.scala
index af9a082945..0043981603 100644
--- a/core/src/main/scala/cats/functor/Bifunctor.scala
+++ b/core/src/main/scala/cats/functor/Bifunctor.scala
@@ -23,8 +23,26 @@ trait Bifunctor[F[_, _]] extends Any with Serializable { self =>
    * apply a function ro the "right" functor
    */
   def rightMap[A,B,C](fab: F[A, B])(f: B => C): F[A,C] = bimap(fab)(identity, f)
+
+  /** The composition of two Bifunctors is itself a Bifunctor */
+  def compose[G[_, _]](implicit G0: Bifunctor[G]): Bifunctor[Lambda[(A, B) => F[G[A, B], G[A, B]]]] =
+    new CompositeBifunctor[F, G] {
+      val F = self
+      val G = G0
+    }
 }
 
 object Bifunctor {
   def apply[F[_, _]](implicit ev: Bifunctor[F]): Bifunctor[F] = ev
 }
+
+trait CompositeBifunctor[F[_, _], G[_, _]]
+    extends Bifunctor[Lambda[(A, B) => F[G[A, B], G[A, B]]]] {
+  def F: Bifunctor[F]
+  def G: Bifunctor[G]
+
+  def bimap[A, B, C, D](fab: F[G[A, B], G[A, B]])(f: A => C, g: B => D): F[G[C, D], G[C, D]] = {
+    val innerBimap: G[A, B] => G[C, D] = gab => G.bimap(gab)(f, g)
+    F.bimap(fab)(innerBimap, innerBimap)
+  }
+}
diff --git a/tests/src/test/scala/cats/tests/BifunctorTests.scala b/tests/src/test/scala/cats/tests/BifunctorTests.scala
new file mode 100644
index 0000000000..b371e72e31
--- /dev/null
+++ b/tests/src/test/scala/cats/tests/BifunctorTests.scala
@@ -0,0 +1,14 @@
+package cats
+package tests
+
+import cats.functor.Bifunctor
+import cats.laws.discipline.{SerializableTests, BifunctorTests}
+
+class BifunctorTest extends CatsSuite {
+  type Tuple2Either[A, B] = (Either[A, B], Either[A, B])
+  val tuple2ComposeEither: Bifunctor[Tuple2Either] =
+    Bifunctor[Tuple2].compose[Either]
+
+  checkAll("Tuple2 compose Either", BifunctorTests(tuple2ComposeEither).bifunctor[Int, Int, Int, String, String, String])
+  checkAll("Bifunctor[Tuple2 compose Either]", SerializableTests.serializable(tuple2ComposeEither))
+}