diff --git a/strings/longest_repeated_substring.py b/strings/longest_repeated_substring.py
new file mode 100644
index 000000000000..2742865f0536
--- /dev/null
+++ b/strings/longest_repeated_substring.py
@@ -0,0 +1,74 @@
+def longest_repeated_substring(s: str) -> str:
+    """
+    Longest repeated (overlapping allowed) substring in O(n) using a suffix automaton.
+    Returns empty string if no repetition.
+    """
+    n = len(s)
+    if n <= 1:
+        return ""
+
+    class State:
+        __slots__ = ("next", "link", "length", "first_pos", "occ")
+
+        def __init__(self):
+            self.next = {}
+            self.link = -1
+            self.length = 0
+            self.first_pos = -1
+            self.occ = 0
+
+    st = [State()]
+    last = 0
+
+    def sa_extend(c, pos):
+        nonlocal last
+        cur = len(st)
+        st.append(State())
+        st[cur].length = st[last].length + 1
+        st[cur].first_pos = pos
+        st[cur].occ = 1
+        p = last
+        while p >= 0 and c not in st[p].next:
+            st[p].next[c] = cur
+            p = st[p].link
+        if p == -1:
+            st[cur].link = 0
+        else:
+            q = st[p].next[c]
+            if st[p].length + 1 == st[q].length:
+                st[cur].link = q
+            else:
+                clone = len(st)
+                st.append(State())
+                st[clone].next = st[q].next.copy()
+                st[clone].length = st[p].length + 1
+                st[clone].link = st[q].link
+                st[clone].first_pos = st[q].first_pos
+                while p >= 0 and st[p].next.get(c) == q:
+                    st[p].next[c] = clone
+                    p = st[p].link
+                st[q].link = clone
+                st[cur].link = clone
+        last = cur
+
+    for i, ch in enumerate(s):
+        sa_extend(ch, i)
+
+    order = sorted(range(len(st)), key=lambda i: st[i].length, reverse=True)
+    for v in order:
+        if st[v].link != -1:
+            st[st[v].link].occ += st[v].occ
+
+    best_len = 0
+    best_end = -1
+    for state in st:
+        if state.occ >= 2 and state.length > best_len:
+            best_len = state.length
+            best_end = state.first_pos
+    if best_len == 0:
+        return ""
+    return s[best_end - best_len + 1 : best_end + 1]
+
+
+if __name__ == "__main__":
+    print(longest_repeated_substring("banana"))