diff --git a/httpcore5/src/main/java/org/apache/hc/core5/http/message/BasicListHeaderIterator.java b/httpcore5/src/main/java/org/apache/hc/core5/http/message/BasicListHeaderIterator.java
index 5cc1b7bb9..c70d5c80f 100644
--- a/httpcore5/src/main/java/org/apache/hc/core5/http/message/BasicListHeaderIterator.java
+++ b/httpcore5/src/main/java/org/apache/hc/core5/http/message/BasicListHeaderIterator.java
@@ -81,6 +81,13 @@ public BasicListHeaderIterator(final List<? extends Header> headers, final Strin
         this.lastIndex = -1;
     }
 
+    BasicListHeaderIterator(final List<? extends Header> headers, final int currentIndex, final String name) {
+        super();
+        this.allHeaders = headers;
+        this.headerName = name;
+        this.currentIndex = currentIndex;
+    }
+
     /**
      * Determines the index of the next header.
      *
diff --git a/httpcore5/src/main/java/org/apache/hc/core5/http/message/HeaderGroup.java b/httpcore5/src/main/java/org/apache/hc/core5/http/message/HeaderGroup.java
index 072ea7ca5..fe010b5ce 100644
--- a/httpcore5/src/main/java/org/apache/hc/core5/http/message/HeaderGroup.java
+++ b/httpcore5/src/main/java/org/apache/hc/core5/http/message/HeaderGroup.java
@@ -345,10 +345,19 @@ public int countHeaders(final String name) {
      *
      * @return iterator over this group of headers.
      *
+     * <p>
+     * IMPORTANT: please note that if the header group mutates while the
+     * iterator returned by this method still has pending elements
+     * the sequence of headers produced by such iterator is considered
+     * unstable and can be incorrect.
+     *
      * @since 5.0
      */
     @Override
     public Iterator<Header> headerIterator() {
+        if (this.headers.isEmpty()) {
+            return NullHeaderIterator.INSTANCE;
+        }
         return new BasicListHeaderIterator(this.headers, null);
     }
 
@@ -360,10 +369,28 @@ public Iterator<Header> headerIterator() {
      *
      * @return iterator over some headers in this group.
      *
+     * <p>
+     * IMPORTANT: please note that if the header group mutates while the
+     * iterator returned by this method still has pending elements
+     * the sequence of headers produced by such iterator is considered
+     * unstable and can be incorrect.
+     *
      * @since 5.0
      */
     @Override
     public Iterator<Header> headerIterator(final String name) {
+        if (this.headers.isEmpty()) {
+            return NullHeaderIterator.INSTANCE;
+        }
+        if (name != null) {
+            for (int i = 0; i < this.headers.size(); i++) {
+                final Header h = this.headers.get(i);
+                if (h.getName().equalsIgnoreCase(name)) {
+                    return new BasicListHeaderIterator(this.headers, i, name);
+                }
+            }
+            return NullHeaderIterator.INSTANCE;
+        }
         return new BasicListHeaderIterator(this.headers, name);
     }
 
diff --git a/httpcore5/src/main/java/org/apache/hc/core5/http/message/NullHeaderIterator.java b/httpcore5/src/main/java/org/apache/hc/core5/http/message/NullHeaderIterator.java
new file mode 100644
index 000000000..dc11c429f
--- /dev/null
+++ b/httpcore5/src/main/java/org/apache/hc/core5/http/message/NullHeaderIterator.java
@@ -0,0 +1,54 @@
+/*
+ * ====================================================================
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you 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.
+ * ====================================================================
+ *
+ * This software consists of voluntary contributions made by many
+ * individuals on behalf of the Apache Software Foundation.  For more
+ * information on the Apache Software Foundation, please see
+ * <http://www.apache.org/>.
+ *
+ */
+
+package org.apache.hc.core5.http.message;
+
+import java.util.Iterator;
+import java.util.NoSuchElementException;
+
+import org.apache.hc.core5.http.Header;
+
+final class NullHeaderIterator implements Iterator<Header> {
+
+    final static NullHeaderIterator INSTANCE = new NullHeaderIterator();
+
+    @Override
+    public boolean hasNext() {
+        return false;
+    }
+
+    @Override
+    public Header next() throws NoSuchElementException {
+        throw new NoSuchElementException("Iteration already finished.");
+    }
+
+    @Override
+    public void remove() throws UnsupportedOperationException {
+        throw new UnsupportedOperationException("Removing headers is not supported.");
+    }
+
+}
diff --git a/httpcore5/src/test/java/org/apache/hc/core5/http/message/TestHeaderGroup.java b/httpcore5/src/test/java/org/apache/hc/core5/http/message/TestHeaderGroup.java
index 9c1b8f83e..21fa97de9 100644
--- a/httpcore5/src/test/java/org/apache/hc/core5/http/message/TestHeaderGroup.java
+++ b/httpcore5/src/test/java/org/apache/hc/core5/http/message/TestHeaderGroup.java
@@ -162,13 +162,49 @@ void testCondensedHeader() {
     }
 
     @Test
-    void testIterator() {
+    void testEmptyListIterator() {
         final HeaderGroup headergroup = new HeaderGroup();
         final Iterator<Header> i = headergroup.headerIterator();
         Assertions.assertNotNull(i);
         Assertions.assertFalse(i.hasNext());
     }
 
+    @Test
+    void testEmptyListIteratorByName() {
+        final HeaderGroup headergroup = new HeaderGroup();
+        final Iterator<Header> i = headergroup.headerIterator("some-header");
+        Assertions.assertNotNull(i);
+        Assertions.assertFalse(i.hasNext());
+    }
+
+    @Test
+    void testNonEmptyListIteratorByName() {
+        final HeaderGroup headergroup = new HeaderGroup();
+        headergroup.setHeaders(
+                new BasicHeader("a", "a-one"),
+                new BasicHeader("b", "b-one"),
+                new BasicHeader("a", "a-two"),
+                new BasicHeader("b", "b-two"),
+                new BasicHeader("b", "b-three"));
+        final Iterator<Header> it1 = headergroup.headerIterator("a");
+        Assertions.assertNotNull(it1);
+        Assertions.assertTrue(it1.hasNext());
+        Assertions.assertEquals("a-one", it1.next().getValue());
+        Assertions.assertTrue(it1.hasNext());
+        Assertions.assertEquals("a-two", it1.next().getValue());
+        Assertions.assertFalse(it1.hasNext());
+
+        final Iterator<Header> it2 = headergroup.headerIterator("b");
+        Assertions.assertNotNull(it2);
+        Assertions.assertTrue(it2.hasNext());
+        Assertions.assertEquals("b-one", it2.next().getValue());
+        Assertions.assertTrue(it2.hasNext());
+        Assertions.assertEquals("b-two", it2.next().getValue());
+        Assertions.assertTrue(it2.hasNext());
+        Assertions.assertEquals("b-three", it2.next().getValue());
+        Assertions.assertFalse(it2.hasNext());
+    }
+
     @Test
     void testHeaderRemove() {
         final HeaderGroup headergroup = new HeaderGroup();