diff --git a/src/stream/mod.rs b/src/stream/mod.rs
index f782882..d8b96ec 100644
--- a/src/stream/mod.rs
+++ b/src/stream/mod.rs
@@ -326,6 +326,7 @@ cfg_unstable! {
     mod interval;
     mod into_stream;
     mod product;
+    mod successors;
     mod sum;
 
     pub use double_ended_stream::DoubleEndedStream;
@@ -337,5 +338,6 @@ cfg_unstable! {
     pub use into_stream::IntoStream;
     pub use product::Product;
     pub use stream::Merge;
+    pub use successors::{successors, Successors};
     pub use sum::Sum;
 }
diff --git a/src/stream/successors.rs b/src/stream/successors.rs
new file mode 100644
index 0000000..d5840ee
--- /dev/null
+++ b/src/stream/successors.rs
@@ -0,0 +1,82 @@
+use std::pin::Pin;
+use std::mem;
+
+use crate::stream::Stream;
+use crate::task::{Context, Poll};
+
+use pin_project_lite::pin_project;
+
+/// Creates a new stream where to produce each new element a closure is called with the previous
+/// value.
+///
+/// # Examples
+///
+/// ```
+/// # fn main() { async_std::task::block_on(async {
+/// #
+/// use async_std::prelude::*;
+/// use async_std::stream;
+///
+/// let s = stream::successors(Some(22), |&val| Some(val + 1) );
+///
+/// pin_utils::pin_mut!(s);
+/// assert_eq!(s.next().await, Some(22));
+/// assert_eq!(s.next().await, Some(23));
+/// assert_eq!(s.next().await, Some(24));
+/// assert_eq!(s.next().await, Some(25));
+///
+/// #
+/// # }) }
+///
+/// ```
+#[cfg(feature = "unstable")]
+#[cfg_attr(feature = "docs", doc(cfg(unstable)))]
+pub fn successors<F, T>(first: Option<T>, succ: F) -> Successors<F, T>
+where
+    F: FnMut(&T) -> Option<T>,
+{
+    Successors {
+        succ,
+        slot: first,
+    }
+}
+
+pin_project! {
+    /// A stream that yields elements by calling an async closure with the previous value as an
+    /// argument
+    ///
+    /// This stream is constructed by [`successors`] function
+    ///
+    /// [`successors`]: fn.succssors.html
+    #[cfg(feature = "unstable")]
+    #[cfg_attr(feature = "docs", doc(cfg(unstable)))]
+    #[derive(Debug)]
+    pub struct Successors<F, T>
+    where
+        F: FnMut(&T) -> Option<T>
+    {
+        succ: F,
+        slot: Option<T>,
+    }
+}
+
+impl<F, T> Stream for Successors<F, T>
+where
+    F: FnMut(&T) -> Option<T>,
+{
+    type Item = T;
+
+    fn poll_next(self: Pin<&mut Self>, _cx: &mut Context<'_>) -> Poll<Option<Self::Item>> {
+        let this = self.project();
+
+        if this.slot.is_none() {
+            return Poll::Ready(None);
+        }
+
+        let mut next = (this.succ)(&this.slot.as_ref().unwrap());
+
+        // 'swapping' here means 'slot' will hold the next value and next will be th one from the previous iteration
+        mem::swap(this.slot, &mut next);
+        Poll::Ready(next)
+    }
+}