diff --git a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/FunctionRegistration.java b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/FunctionRegistration.java
index 8907c6ee9..484f36011 100644
--- a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/FunctionRegistration.java
+++ b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/FunctionRegistration.java
@@ -1,5 +1,5 @@
 /*
- * Copyright 2012-2019 the original author or authors.
+ * Copyright 2016-2019 the original author or authors.
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
@@ -153,30 +153,27 @@ public class FunctionRegistration<T> implements BeanNameAware {
 			S target = (S) this.target;
 			result = new FunctionRegistration<S>(target);
 			result.type(this.type.getType());
-			boolean flux = type.isWrapper();
-			if (!flux) {
-				if (target instanceof Function) {
-					target = (S) new FluxFunction((Function<?, ?>) target);
-				}
-				else if (target instanceof Supplier) {
-					target = (S) new FluxSupplier((Supplier<?>) target);
-				}
-				else if (target instanceof Consumer) {
-					target = (S) new FluxConsumer((Consumer<?>) target);
-				}
-			}
-			else {
-				if (target instanceof Consumer) {
-					target = (S) new FluxedConsumer((Consumer<?>) target);
-				}
-			}
 
-			if (Mono.class.isAssignableFrom(type.getOutputWrapper())) {
+			if (!type.isWrapper()) {
+				target = target instanceof Supplier
+						? (S) new FluxSupplier((Supplier<?>) target)
+						: target instanceof Function
+								? (S) new FluxFunction((Function<?, ?>) target)
+								: (S) new FluxConsumer((Consumer<?>) target);
+			}
+			else if (Mono.class.isAssignableFrom(type.getOutputWrapper())) {
 				target = (S) new FluxToMonoFunction((Function) target);
 			}
 			else if (Mono.class.isAssignableFrom(type.getInputWrapper())) {
 				target = (S) new MonoToFluxFunction((Function) target);
 			}
+			else if (target instanceof Consumer) {
+				target = (S) new FluxedConsumer((Consumer<?>) target);
+			}
+			else if (target instanceof Function) {
+				// target = (S) new FluxedFunction((Function<?, ?>) target);
+			}
+
 			result = result.target(target).names(this.names)
 					.type(result.type.wrap(Flux.class)).properties(this.properties);
 		}
diff --git a/spring-cloud-function-core/src/main/java/org/springframework/cloud/function/core/FluxToMonoFunction.java b/spring-cloud-function-core/src/main/java/org/springframework/cloud/function/core/FluxToMonoFunction.java
index 07c23790f..cfff5d9fa 100644
--- a/spring-cloud-function-core/src/main/java/org/springframework/cloud/function/core/FluxToMonoFunction.java
+++ b/spring-cloud-function-core/src/main/java/org/springframework/cloud/function/core/FluxToMonoFunction.java
@@ -22,7 +22,7 @@ import reactor.core.publisher.Flux;
 import reactor.core.publisher.Mono;
 
 /**
- * Marker wrapper for target Function&lt;Flux, Mono&gt;.
+ * Marker wrapper for target {@code Function<Flux<?>, Mono<?>>}.
  *
  * @param <I> type of {@link Flux} input of the target function
  * @param <O> type of {@link Mono} output of the target function
diff --git a/spring-cloud-function-core/src/main/java/org/springframework/cloud/function/core/FluxedFunction.java b/spring-cloud-function-core/src/main/java/org/springframework/cloud/function/core/FluxedFunction.java
new file mode 100644
index 000000000..a1aeae979
--- /dev/null
+++ b/spring-cloud-function-core/src/main/java/org/springframework/cloud/function/core/FluxedFunction.java
@@ -0,0 +1,44 @@
+/*
+ * Copyright 2019-2019 the original author or authors.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.springframework.cloud.function.core;
+
+import java.util.function.Function;
+
+import reactor.core.publisher.Flux;
+
+/**
+ * {@link Function} implementation that wraps a target Function so that the target's
+ * simple input and output types will be wrapped as {@link Flux} instances.
+ *
+ * @param <T> input type of target function
+ * @param <R> output type of target function
+ * @author Oleg Zhurakousky
+ * @since 2.0.1
+ */
+public class FluxedFunction<I, O>
+		extends WrappedFunction<I, O, Flux<I>, Flux<O>, Function<Flux<I>, Flux<O>>> {
+
+	public FluxedFunction(Function<Flux<I>, Flux<O>> target) {
+		super(target);
+	}
+
+	@Override
+	public Flux<O> apply(Flux<I> input) {
+		return input.transform(this.getTarget());
+	}
+
+}