diff --git a/sortedcontainers/sorteddict.py b/sortedcontainers/sorteddict.py
index 320b861..fdaca13 100644
--- a/sortedcontainers/sorteddict.py
+++ b/sortedcontainers/sorteddict.py
@@ -512,6 +512,33 @@ def peekitem(self, index=-1):
         key = self._list[index]
         return key, self[key]
 
+    def next_smaller_item(self, value):
+        """Return strictly smaller item than the given key."""
+        i = self.bisect_left(value) - 1
+        if i < 0:
+            return None, None
+        return self.peekitem(index=i)
+
+    def floor_item(self, value):
+        """Return smaller or equal item than the given key."""
+        i = self.bisect_right(value) - 1
+        if i < 0:
+            return None, None
+        return self.peekitem(index=i)
+
+    def ceil_item(self, value):
+        """Return larger or equal item than the given key."""
+        i = self.bisect_left(value)
+        if i >= len(self):
+            return None, None
+        return self.peekitem(index=i)
+
+    def next_greater_item(self, value):
+        """Return strictly larger item than the given key."""
+        i = self.bisect_right(value)
+        if i >= len(self):
+            return None, None
+        return self.peekitem(index=i)
 
     def setdefault(self, key, default=None):
         """Return value for item identified by `key` in sorted dict.
diff --git a/sortedcontainers/sortedlist.py b/sortedcontainers/sortedlist.py
index e3b58eb..a857722 100644
--- a/sortedcontainers/sortedlist.py
+++ b/sortedcontainers/sortedlist.py
@@ -1229,6 +1229,33 @@ def bisect_right(self, value):
     bisect = bisect_right
     _bisect_right = bisect_right
 
+    def next_smaller(self, value):
+        """Return strictly smaller value to the given value."""
+        i = self.bisect_left(value) - 1
+        if i < 0:
+            return None
+        return self[i]
+
+    def floor(self, value):
+        """Return smaller or equal value than the given value."""
+        i = self.bisect_right(value) - 1
+        if i < 0:
+            return None
+        return self[i]
+
+    def ceil(self, value):
+        """Return larger or equal value than the given value."""
+        i = self.bisect_left(value)
+        if i >= len(self):
+            return None
+        return self[i]
+
+    def next_greater(self, value):
+        """Return strictly larger value than the given value."""
+        i = self.bisect_right(value)
+        if i >= len(self):
+            return None
+        return self[i]
 
     def count(self, value):
         """Return number of occurrences of `value` in the sorted list.
diff --git a/sortedcontainers/sortedset.py b/sortedcontainers/sortedset.py
index be2b899..7fdac11 100644
--- a/sortedcontainers/sortedset.py
+++ b/sortedcontainers/sortedset.py
@@ -153,6 +153,10 @@ def __init__(self, iterable=None, key=None):
         self.bisect_left = _list.bisect_left
         self.bisect = _list.bisect
         self.bisect_right = _list.bisect_right
+        self.next_smaller = _list.next_smaller
+        self.floor = _list.floor
+        self.ceil = _list.ceil
+        self.next_greater = _list.next_greater
         self.index = _list.index
         self.irange = _list.irange
         self.islice = _list.islice
diff --git a/tests/test_coverage_sorteddict.py b/tests/test_coverage_sorteddict.py
index 9b62a7f..47bcc1c 100644
--- a/tests/test_coverage_sorteddict.py
+++ b/tests/test_coverage_sorteddict.py
@@ -357,6 +357,48 @@ def test_bisect_key2():
     assert all(temp.bisect_key_right(val) == ((val % 10) + 1) * 10 for val in range(10))
     assert all(temp.bisect_key_left(val) == (val % 10) * 10 for val in range(10))
 
+
+# Test Values for adjacent search functions.
+sd = SortedDict({1: "a", 2: "b", 4: "c", 5: "d"})
+k1 = 0  # The key that is smaller than any existing value.
+k2 = 1  # The key that is the smallest in the instance.
+k3 = 3  # The key that does not exists in the instance.
+k4 = 4  # The key that exists in the instance.
+k5 = 5  # The key that is the largest in the instance.
+k6 = 6  # The key that is larger than any existing value.
+
+def test_next_smaller_item():
+    assert sd.next_smaller_item(k1) == (None, None)
+    assert sd.next_smaller_item(k2) == (None, None)
+    assert sd.next_smaller_item(k3) == (2, "b")
+    assert sd.next_smaller_item(k4) == (2, "b")
+    assert sd.next_smaller_item(k5) == (4, "c")
+    assert sd.next_smaller_item(k6) == (5, "d")
+
+def test_floor_item():
+    assert sd.floor_item(k1) == (None, None)
+    assert sd.floor_item(k2) == (1, "a")
+    assert sd.floor_item(k3) == (2, "b")
+    assert sd.floor_item(k4) == (4, "c")
+    assert sd.floor_item(k5) == (5, "d")
+    assert sd.floor_item(k6) == (5, "d")
+
+def test_ceil_item():
+    assert sd.ceil_item(k1) == (1, "a")
+    assert sd.ceil_item(k2) == (1, "a")
+    assert sd.ceil_item(k3) == (4, "c")
+    assert sd.ceil_item(k4) == (4, "c")
+    assert sd.ceil_item(k5) == (5, "d")
+    assert sd.ceil_item(k6) == (None, None)
+
+def test_next_greater_item():
+    assert sd.next_greater_item(k1) == (1, "a")
+    assert sd.next_greater_item(k2) == (2, "b")
+    assert sd.next_greater_item(k3) == (4, "c")
+    assert sd.next_greater_item(k4) == (5, "d")
+    assert sd.next_greater_item(k5) == (None, None)
+    assert sd.next_greater_item(k6) == (None, None)
+
 def test_keysview():
     mapping = [(val, pos) for pos, val in enumerate(string.ascii_lowercase)]
     temp = SortedDict(mapping[:13])
diff --git a/tests/test_coverage_sortedlist.py b/tests/test_coverage_sortedlist.py
index 7e009e1..f8bbf4d 100644
--- a/tests/test_coverage_sortedlist.py
+++ b/tests/test_coverage_sortedlist.py
@@ -368,6 +368,48 @@ def test_bisect_right():
     assert slt.bisect_right(10) == 22
     assert slt.bisect_right(200) == 200
 
+
+# Test Values for adjacent search functions.
+slt = SortedList([1, 2, 4, 4, 5])
+v1 = 0  # The value that is smaller than any existing value.
+v2 = 1  # The value that is the smallest in the instance.
+v3 = 3  # The value that does not exists in the instance.
+v4 = 4  # The value that exists in the instance.
+v5 = 5  # The value that is the largest in the instance.
+v6 = 6  # The value that is larger than any existing value.
+
+def test_next_smaller():
+    assert slt.next_smaller(v1) is None
+    assert slt.next_smaller(v2) is None
+    assert slt.next_smaller(v3) == 2
+    assert slt.next_smaller(v4) == 2
+    assert slt.next_smaller(v5) == 4
+    assert slt.next_smaller(v6) == 5
+
+def test_floor():
+    assert slt.floor(v1) is None
+    assert slt.floor(v2) == 1
+    assert slt.floor(v3) == 2
+    assert slt.floor(v4) == 4
+    assert slt.floor(v5) == 5
+    assert slt.floor(v6) == 5
+
+def test_ceil():
+    assert slt.ceil(v1) == 1
+    assert slt.ceil(v2) == 1
+    assert slt.ceil(v3) == 4
+    assert slt.ceil(v4) == 4
+    assert slt.ceil(v5) == 5
+    assert slt.ceil(v6) is None
+
+def test_next_greater():
+    assert slt.next_greater(v1) == 1
+    assert slt.next_greater(v2) == 2
+    assert slt.next_greater(v3) == 4
+    assert slt.next_greater(v4) == 5
+    assert slt.next_greater(v5) is None
+    assert slt.next_greater(v6) is None
+
 def test_copy():
     alpha = SortedList(range(100))
     alpha._reset(7)
diff --git a/tests/test_coverage_sortedset.py b/tests/test_coverage_sortedset.py
index e67487d..a6d2cf4 100644
--- a/tests/test_coverage_sortedset.py
+++ b/tests/test_coverage_sortedset.py
@@ -255,6 +255,48 @@ def test_bisect_key():
     assert all(temp.bisect_key(val) == (val + 1) for val in range(100))
     assert all(temp.bisect_key_right(val) == (val + 1) for val in range(100))
 
+
+# Test Values for adjacent search functions.
+ss = SortedSet([1, 2, 4, 5])
+v1 = 0  # The value that is smaller than any existing value.
+v2 = 1  # The value that is the smallest in the instance.
+v3 = 3  # The value that does not exists in the instance.
+v4 = 4  # The value that exists in the instance.
+v5 = 5  # The value that is the largest in the instance.
+v6 = 6  # The value that is larger than any existing value.
+
+def test_next_smaller():
+    assert ss.next_smaller(v1) is None
+    assert ss.next_smaller(v2) is None
+    assert ss.next_smaller(v3) == 2
+    assert ss.next_smaller(v4) == 2
+    assert ss.next_smaller(v5) == 4
+    assert ss.next_smaller(v6) == 5
+
+def test_floor():
+    assert ss.floor(v1) is None
+    assert ss.floor(v2) == 1
+    assert ss.floor(v3) == 2
+    assert ss.floor(v4) == 4
+    assert ss.floor(v5) == 5
+    assert ss.floor(v6) == 5
+
+def test_ceil():
+    assert ss.ceil(v1) == 1
+    assert ss.ceil(v2) == 1
+    assert ss.ceil(v3) == 4
+    assert ss.ceil(v4) == 4
+    assert ss.ceil(v5) == 5
+    assert ss.ceil(v6) is None
+
+def test_next_greater():
+    assert ss.next_greater(v1) == 1
+    assert ss.next_greater(v2) == 2
+    assert ss.next_greater(v3) == 4
+    assert ss.next_greater(v4) == 5
+    assert ss.next_greater(v5) is None
+    assert ss.next_greater(v6) is None
+
 def test_clear():
     temp = SortedSet(range(100))
     temp._reset(7)