diff --git a/libraries/stdlib/src/kotlin/Iterators.kt b/libraries/stdlib/src/kotlin/Iterators.kt
index e501eeefb0d..ce64ba62e39 100644
--- a/libraries/stdlib/src/kotlin/Iterators.kt
+++ b/libraries/stdlib/src/kotlin/Iterators.kt
@@ -2,6 +2,7 @@ package kotlin
 
 import kotlin.support.*
 import java.util.Collections
+import kotlin.test.assertTrue
 
 /**
  * Returns an iterator which invokes the function to calculate the next value on each iteration until the function returns *null*
@@ -10,6 +11,23 @@ public inline fun <T:Any> iterate(nextFunction: () -> T?) : Iterator<T> {
     return FunctionIterator(nextFunction)
 }
 
+/**
+ * Returns an iterator which invokes the function to calculate the next value based on the previous one on each iteration
+ * until the function returns *null*
+ */
+public inline fun <T: Any> iterate(initialValue: T, nextFunction: (T) -> T?): Iterator<T> =
+        iterate(nextFunction.toGenerator(initialValue))
+
+/**
+ * Returns an iterator whose values are pairs composed of values produced by given pair of iterators
+ */
+public inline fun <T, S> Iterator<T>.zip(iterator: Iterator<S>): Iterator<Pair<T, S>> = PairIterator(this, iterator)
+
+/**
+ * Returns an iterator shifted to right by the given number of elements
+ */
+public inline fun <T> Iterator<T>.skip(n: Int): Iterator<T> = SkippingIterator(this, n)
+
 class FilterIterator<T>(val iterator : Iterator<T>, val predicate: (T)-> Boolean) : AbstractIterator<T>() {
     override protected fun computeNext(): Unit {
         while (iterator.hasNext()) {
@@ -147,3 +165,50 @@ class IndexIterator<T>(val iterator : Iterator<T>): Iterator<Pair<Int, T>> {
         return iterator.hasNext()
     }
 }
+
+public class PairIterator<T, S>(
+        val iterator1 : Iterator<T>, val iterator2 : Iterator<S>
+): AbstractIterator<Pair<T, S>>() {
+    protected override fun computeNext() {
+        if (iterator1.hasNext() && iterator2.hasNext()) {
+            setNext(Pair(iterator1.next(), iterator2.next()))
+        }
+        else {
+            done()
+        }
+    }
+}
+
+class SkippingIterator<T>(val iterator: Iterator<T>, val n: Int): Iterator<T> {
+    private var firstTime: Boolean = true
+
+    private fun skip() {
+        for (i in 1..n) {
+            if (!iterator.hasNext()) break
+            iterator.next()
+        }
+        firstTime = false
+    }
+
+    override fun next(): T {
+        assertTrue(!firstTime, "hasNext() must be invoked before advancing an iterator")
+        return iterator.next()
+    }
+
+    override fun hasNext(): Boolean {
+        if (firstTime) {
+            skip()
+        }
+        return iterator.hasNext()
+    }
+}
+
+fun <T: Any> Function1<T, T?>.toGenerator(initialValue: T): Function0<T?> {
+    var nextValue: T? = initialValue
+    return {
+        nextValue?.let { result ->
+            nextValue = this@toGenerator(result)
+            result
+        }
+    }
+}
\ No newline at end of file
diff --git a/libraries/stdlib/test/iterators/FunctionIteratorTest.kt b/libraries/stdlib/test/iterators/FunctionIteratorTest.kt
index b1aa318ff55..8b788be839b 100644
--- a/libraries/stdlib/test/iterators/FunctionIteratorTest.kt
+++ b/libraries/stdlib/test/iterators/FunctionIteratorTest.kt
@@ -18,4 +18,9 @@ class FunctionIteratorTest {
         val list = iter.toList()
         assertEquals(arrayList(2, 1, 0), list)
     }
+
+    Test fun iterateOverFunction2() {
+        val values = iterate<Int>(3) { n -> if (n > 0) n - 1 else null }
+        assertEquals(arrayList(3, 2, 1, 0), values.toList())
+    }
 }
\ No newline at end of file
diff --git a/libraries/stdlib/test/iterators/IteratorsTest.kt b/libraries/stdlib/test/iterators/IteratorsTest.kt
index fae3fc23b97..831678ea997 100644
--- a/libraries/stdlib/test/iterators/IteratorsTest.kt
+++ b/libraries/stdlib/test/iterators/IteratorsTest.kt
@@ -77,4 +77,14 @@ class IteratorsTest {
         assertEquals("13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...", fibonacci().filter {  it > 10 }.makeString(limit = 10))
         assertEquals("144, 233, 377, 610, 987", fibonacci().filter { it > 100 }.takeWhile { it < 1000 }.makeString())
     }
+
+    test fun pairIterator() {
+        val pairStr = (fibonacci() zip fibonacci().map { i -> i*2 }).makeString(limit = 10)
+        assertEquals("(0, 0), (1, 2), (1, 2), (2, 4), (3, 6), (5, 10), (8, 16), (13, 26), (21, 42), (34, 68), ...", pairStr)
+    }
+
+    test fun skippingIterator() {
+        assertEquals("13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...", fibonacci().skip(7).makeString(limit = 10))
+        assertEquals("13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...", fibonacci().skip(3).skip(4).makeString(limit = 10))
+    }
 }