diff --git a/src/core/CCFun.ml b/src/core/CCFun.ml
index 65c9a5d5..d70c00b7 100644
--- a/src/core/CCFun.ml
+++ b/src/core/CCFun.ml
@@ -77,7 +77,11 @@ struct
   type 'a t = X.t -> 'a
 
   let[@inline] return x _ = x
+  let[@inline] k_compose f g =
+    (fun x -> f x |> flat_map g)
   let[@inline] ( >|= ) f g x = g (f x)
   let[@inline] ( >>= ) f g x = g (f x) x
+  let[@inline] ( >=> ) = k_compose
+  let[@inline] ( <=< ) = flip k_compose
 end
 [@@inline]
diff --git a/src/core/CCFun.mli b/src/core/CCFun.mli
index 1557f780..2cd4774e 100644
--- a/src/core/CCFun.mli
+++ b/src/core/CCFun.mli
@@ -105,8 +105,18 @@ end) : sig
   val return : 'a -> 'a t
   (** Monadic [return]. *)
 
+  val k_compose : ('a -> 'b t) -> ('b -> 'c t) -> ('a -> 'c t)
+  (** Kleisli composition. Monadic equivalent of [compose]. *)
+
   val ( >|= ) : 'a t -> ('a -> 'b) -> 'b t
+  (** Mondaic [map]. *)
 
   val ( >>= ) : 'a t -> ('a -> 'b t) -> 'b t
   (** Monadic [bind]. *)
+
+  val ( >=> ) : ('a -> 'b t) -> ('b -> 'c t) -> ('a -> 'c t)
+  (** Monadic [k_compose]. *)
+
+  val ( <=< ) : ('b -> 'c t) -> ('a -> 'b t) -> ('a -> 'c t)
+  (** Reverse monadic [k_compose]. *)
 end
diff --git a/src/core/CCOption.ml b/src/core/CCOption.ml
index 10bd4239..6bc1ddde 100644
--- a/src/core/CCOption.ml
+++ b/src/core/CCOption.ml
@@ -55,6 +55,11 @@ let[@inline] bind o f = flat_map f o
 let ( >>= ) = bind
 let pure x = Some x
 
+let k_compose f g =
+  (fun x -> f x |> flat_map g)
+let ( >=> ) = k_compose
+let ( <=< ) f g = (>=>) g f 
+
 let ( <*> ) f x =
   match f, x with
   | None, _ | _, None -> None
@@ -190,6 +195,10 @@ module Infix = struct
     | _ -> None
 
   let ( and* ) = ( and+ )
+
+  let ( >=> ) = ( >=> )
+
+  let ( <=< ) = ( <=< )
 end
 
 include Infix
diff --git a/src/core/CCOption.mli b/src/core/CCOption.mli
index 06ad03d9..e1f8d30a 100644
--- a/src/core/CCOption.mli
+++ b/src/core/CCOption.mli
@@ -58,6 +58,9 @@ val bind : 'a t -> ('a -> 'b t) -> 'b t
     Monadic bind.
     @since 3.0 *)
 
+val k_compose : ('a -> 'b t) -> ('b -> 'c t) -> ('a -> 'c t)
+(** Kleisli composition. Monadic equivalent of CCFun.compose *)
+
 val map2 : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t
 (** [map2 f o1 o2] maps ['a option] and ['b option] to a ['c option] using [f]. *)
 
@@ -179,6 +182,11 @@ module Infix : sig
   val ( and+ ) : 'a t -> 'b t -> ('a * 'b) t
   val ( let* ) : 'a t -> ('a -> 'b t) -> 'b t
   val ( and* ) : 'a t -> 'b t -> ('a * 'b) t
+
+  val ( >=> ) : ('a -> 'b t) -> ('b -> 'c t) -> ('a -> 'c t)
+  (** Monadic [k_compose]. *)
+  val ( <=< ) : ('b -> 'c t) -> ('a -> 'b t) -> ('a -> 'c t)
+  (** Reverse monadic [k_compose]. *)
 end
 
 include module type of Infix
diff --git a/src/core/CCResult.ml b/src/core/CCResult.ml
index 9acb529b..4f743600 100644
--- a/src/core/CCResult.ml
+++ b/src/core/CCResult.ml
@@ -125,6 +125,12 @@ let flat_map f e =
   | Ok x -> f x
   | Error s -> Error s
 
+let k_compose f g =
+  (fun x -> flat_map g @@ f x)
+
+let ( >=> ) = k_compose
+let ( <=< ) f g = ( >=> ) g f 
+
 let equal ~err eq a b =
   match a, b with
   | Ok x, Ok y -> eq x y
@@ -275,6 +281,9 @@ module Infix = struct
     | _, Error e -> Error e
 
   let ( and* ) = ( and+ )
+
+  let ( >=> ) = ( >=> )
+  let ( <=< ) = ( <=< )
 end
 
 include Infix
diff --git a/src/core/CCResult.mli b/src/core/CCResult.mli
index 50b7fb68..171bc273 100644
--- a/src/core/CCResult.mli
+++ b/src/core/CCResult.mli
@@ -113,6 +113,10 @@ val catch : ('a, 'err) t -> ok:('a -> 'b) -> err:('err -> 'b) -> 'b
     the value of [e]. *)
 
 val flat_map : ('a -> ('b, 'err) t) -> ('a, 'err) t -> ('b, 'err) t
+
+val k_compose : ('a -> ('b, 'err) t) -> ('b -> ('c, 'err) t) -> ('a -> ('c, 'err) t)
+(** Kleisli composition. Monadic equivalent of CCFun.compose *)
+
 val equal : err:'err equal -> 'a equal -> ('a, 'err) t equal
 val compare : err:'err ord -> 'a ord -> ('a, 'err) t ord
 
@@ -199,6 +203,11 @@ module Infix : sig
 
   val ( and* ) : ('a, 'e) t -> ('b, 'e) t -> ('a * 'b, 'e) t
   (** @since 2.8 *)
+
+  val ( >=> ) : ('a -> ('b, 'err) t) -> ('b -> ('c, 'err) t) -> ('a -> ('c, 'err) t)
+  (** Monadic [k_compose]. *)
+  val ( <=< ) : ('b -> ('c, 'err) t) -> ('a -> ('b, 'err) t) -> ('a -> ('c, 'err) t)
+  (** Reverse monadic [k_compose]. *)
 end
 
 include module type of Infix