diff --git a/akka-stream/src/main/scala/akka/stream/scaladsl/Flow.scala b/akka-stream/src/main/scala/akka/stream/scaladsl/Flow.scala
index 5deebf282f..1f59f6a48f 100644
--- a/akka-stream/src/main/scala/akka/stream/scaladsl/Flow.scala
+++ b/akka-stream/src/main/scala/akka/stream/scaladsl/Flow.scala
@@ -221,15 +221,24 @@ final class Flow[-In, +Out, +Mat](private[stream] override val module: Module)
    * The resulting Flow’s materialized value is a Tuple2 containing both materialized
    * values (of this Flow and that Source).
    */
-  def concat[Out2 >: Out, Mat2](source: Source[Out2, Mat2]): Flow[In, Out2, (Mat, Mat2)] = {
+  def concat[Out2 >: Out, Mat2](source: Source[Out2, Mat2]): Flow[In, Out2, (Mat, Mat2)] =
+    concatMat[Out2, Mat2, (Mat, Mat2)](source, Keep.both)
+
+  /**
+   * Concatenate the given [[Source]] to this [[Flow]], meaning that once this
+   * Flow’s input is exhausted and all result elements have been generated,
+   * the Source’s elements will be produced. Note that the Source is materialized
+   * together with this Flow and just kept from producing elements by asserting
+   * back-pressure until its time comes.
+   */
+  def concatMat[Out2 >: Out, Mat2, Mat3](source: Source[Out2, Mat2], combine: (Mat, Mat2) ⇒ Mat3): Flow[In, Out2, Mat3] =
     this.viaMat(Flow(source) { implicit builder ⇒
       s ⇒
         import FlowGraph.Implicits._
         val concat = builder.add(Concat[Out2]())
         s.outlet ~> concat.in(1)
         (concat.in(0), concat.out)
-    })(Keep.both)
-  }
+    })(combine)
 
   /** INTERNAL API */
   override private[stream] def andThen[U](op: StageModule): Repr[U, Mat] = {
diff --git a/akka-stream/src/main/scala/akka/stream/scaladsl/Source.scala b/akka-stream/src/main/scala/akka/stream/scaladsl/Source.scala
index 54fb7ca5b2..917bca52b5 100644
--- a/akka-stream/src/main/scala/akka/stream/scaladsl/Source.scala
+++ b/akka-stream/src/main/scala/akka/stream/scaladsl/Source.scala
@@ -125,7 +125,15 @@ final class Source[+Out, +Mat](private[stream] override val module: Module)
    * emitted by that source is emitted after the last element of this
    * source.
    */
-  def concat[Out2 >: Out, M](second: Source[Out2, M]): Source[Out2, (Mat, M)] = Source.concat(this, second)
+  def concat[Out2 >: Out, M](second: Source[Out2, M]): Source[Out2, (Mat, M)] = concatMat(second)(Keep.both)
+
+  /**
+   * Concatenates a second source so that the first element
+   * emitted by that source is emitted after the last element of this
+   * source.
+   */
+  def concatMat[Out2 >: Out, Mat2, Mat3](second: Source[Out2, Mat2])(
+    combine: (Mat, Mat2) ⇒ Mat3): Source[Out2, Mat3] = Source.concatMat(this, second)(combine)
 
   /**
    * Concatenates a second source so that the first element
@@ -304,7 +312,16 @@ object Source extends SourceApply {
    * source.
    */
   def concat[T, Mat1, Mat2](source1: Source[T, Mat1], source2: Source[T, Mat2]): Source[T, (Mat1, Mat2)] =
-    wrap(FlowGraph.partial(source1, source2)(Keep.both) { implicit b ⇒
+    concatMat(source1, source2)(Keep.both)
+
+  /**
+   * Concatenates two sources so that the first element
+   * emitted by the second source is emitted after the last element of the first
+   * source.
+   */
+  def concatMat[T, Mat1, Mat2, Mat3](source1: Source[T, Mat1], source2: Source[T, Mat2])(
+    combine: (Mat1, Mat2) ⇒ Mat3): Source[T, Mat3] =
+    wrap(FlowGraph.partial(source1, source2)(combine) { implicit b ⇒
       (s1, s2) ⇒
         import FlowGraph.Implicits._
         val c = b.add(Concat[T]())