diff --git a/Doc/library/io.rst b/Doc/library/io.rst
--- a/Doc/library/io.rst
+++ b/Doc/library/io.rst
@@ -301,6 +301,10 @@
       .. versionadded:: 3.1
          The ``SEEK_*`` constants.
 
+      .. versionadded:: 3.2
+         Some Operating Systems can support aditional values, like
+         :const:`os.SEEK_HOLE` or :const:`os.SEEK_DATA`.
+
    .. method:: seekable()
 
       Return ``True`` if the stream supports random access.  If ``False``,
diff --git a/Doc/library/os.rst b/Doc/library/os.rst
--- a/Doc/library/os.rst
+++ b/Doc/library/os.rst
@@ -716,6 +716,10 @@
    Parameters to the :func:`lseek` function. Their values are 0, 1, and 2,
    respectively. Availability: Windows, Unix.
 
+   .. versionadded:: 3.2
+      Some Operating Systems can support aditional values, like
+      :const:`os.SEEK_HOLE` or :const:`os.SEEK_DATA`.
+
 
 .. function:: open(file, flags[, mode])
 
diff --git a/Lib/os.py b/Lib/os.py
--- a/Lib/os.py
+++ b/Lib/os.py
@@ -110,6 +110,7 @@
 
 # Python uses fixed values for the SEEK_ constants; they are mapped
 # to native constants if necessary in posixmodule.c
+# Other possible SEEK values are directly imported from posixmodule.c
 SEEK_SET = 0
 SEEK_CUR = 1
 SEEK_END = 2
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -637,13 +637,6 @@
         # this test. Else, write it.
         pass
 
-    def test_invalid_args(self):
-        rawio = self.MockRawIO()
-        bufio = self.tp(rawio)
-        # Invalid whence
-        self.assertRaises(ValueError, bufio.seek, 0, -1)
-        self.assertRaises(ValueError, bufio.seek, 0, 3)
-
     def test_override_destructor(self):
         tp = self.tp
         record = []
diff --git a/Misc/NEWS b/Misc/NEWS
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -290,6 +290,8 @@
 
 - Issue #9377: Use Unicode API for gethostname on Windows.
 
+- Issue #10142: Support for SEEK_HOLE/SEEK_DATA (for example, under ZFS).
+
 - Issue #10143: Update "os.pathconf" values.
 
 - Issue #6518: Support context manager protcol for ossaudiodev types.
diff --git a/Modules/_io/bufferedio.c b/Modules/_io/bufferedio.c
--- a/Modules/_io/bufferedio.c
+++ b/Modules/_io/bufferedio.c
@@ -1018,11 +1018,6 @@
     if (!PyArg_ParseTuple(args, "O|i:seek", &targetobj, &whence)) {
         return NULL;
     }
-    if (whence < 0 || whence > 2) {
-        PyErr_Format(PyExc_ValueError,
-                     "whence must be between 0 and 2, not %d", whence);
-        return NULL;
-    }
 
     CHECK_CLOSED(self, "seek of closed file")
 
@@ -1030,7 +1025,11 @@
     if (target == -1 && PyErr_Occurred())
         return NULL;
 
-    if (whence != 2 && self->readable) {
+    /* SEEK_SET and SEEK_CUR are special because we could seek inside the
+       buffer. Other whence values must be managed without this optimization.
+       Some Operating Systems can provide additional values, like
+       SEEK_HOLE/SEEK_DATA. */
+    if (((whence == 0) || (whence == 1)) && self->readable) {
         Py_off_t current, avail;
         /* Check if seeking leaves us inside the current buffer,
            so as to return quickly if possible. Also, we needn't take the
diff --git a/Modules/posixmodule.c b/Modules/posixmodule.c
--- a/Modules/posixmodule.c
+++ b/Modules/posixmodule.c
@@ -8151,6 +8151,13 @@
     if (ins(d, "O_EXLOCK", (long)O_EXLOCK)) return -1;
 #endif
 
+#ifdef SEEK_HOLE /* ZFS */
+    if (ins(d, "SEEK_HOLE", (long)SEEK_HOLE)) return -1;
+#endif
+#ifdef SEEK_DATA /* ZFS */
+    if (ins(d, "SEEK_DATA", (long)SEEK_DATA)) return -1;
+#endif
+
 /* MS Windows */
 #ifdef O_NOINHERIT
     /* Don't inherit in child processes. */