diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index be3f11ea4da1f..1b319e12f06d5 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -368,12 +368,31 @@ class _BaseOffset(object):
                 if name not in ['n', 'normalize']}
         return {name: kwds[name] for name in kwds if kwds[name] is not None}
 
+    def __add__(self, other):
+        if getattr(other, "_typ", None) in ["datetimeindex",
+                                            "series", "period"]:
+            # defer to the other class's implementation
+            return other + self
+        try:
+            return self.apply(other)
+        except ApplyTypeError:
+            return NotImplemented
+
+    def __sub__(self, other):
+        if isinstance(other, datetime):
+            raise TypeError('Cannot subtract datetime from offset.')
+        elif type(other) == type(self):
+            return type(self)(self.n - other.n, normalize=self.normalize,
+                              **self.kwds)
+        else:  # pragma: no cover
+            return NotImplemented
+
     def __call__(self, other):
         return self.apply(other)
 
     def __mul__(self, other):
-        return self.__class__(n=other * self.n, normalize=self.normalize,
-                              **self.kwds)
+        return type(self)(n=other * self.n, normalize=self.normalize,
+                          **self.kwds)
 
     def __neg__(self):
         # Note: we are defering directly to __mul__ instead of __rmul__, as
@@ -495,6 +514,14 @@ class BaseOffset(_BaseOffset):
         return -self + other
 
 
+class _Tick(object):
+    """
+    dummy class to mix into tseries.offsets.Tick so that in tslibs.period we
+    can do isinstance checks on _Tick and avoid importing tseries.offsets
+    """
+    pass
+
+
 # ----------------------------------------------------------------------
 # RelativeDelta Arithmetic
 
diff --git a/pandas/_libs/tslibs/period.pyx b/pandas/_libs/tslibs/period.pyx
index 6e5794ef41757..3a29f9fb00865 100644
--- a/pandas/_libs/tslibs/period.pyx
+++ b/pandas/_libs/tslibs/period.pyx
@@ -52,8 +52,7 @@ from resolution import Resolution
 from nattype import nat_strings, NaT, iNaT
 from nattype cimport _nat_scalar_rules, NPY_NAT, is_null_datetimelike
 from offsets cimport to_offset
-
-from pandas.tseries import offsets
+from offsets import _Tick
 
 cdef bint PY2 = str == bytes
 
@@ -1060,9 +1059,9 @@ cdef class _Period(object):
             int64_t nanos, offset_nanos
 
         if (PyDelta_Check(other) or util.is_timedelta64_object(other) or
-                isinstance(other, offsets.Tick)):
+                isinstance(other, _Tick)):
             offset = to_offset(self.freq.rule_code)
-            if isinstance(offset, offsets.Tick):
+            if isinstance(offset, _Tick):
                 nanos = delta_to_nanoseconds(other)
                 offset_nanos = delta_to_nanoseconds(offset)
                 if nanos % offset_nanos == 0:
diff --git a/pandas/tseries/offsets.py b/pandas/tseries/offsets.py
index f9c9ec09844d6..d78d199f1404b 100644
--- a/pandas/tseries/offsets.py
+++ b/pandas/tseries/offsets.py
@@ -7,7 +7,7 @@
 from pandas import compat
 import numpy as np
 
-from pandas.core.dtypes.generic import ABCSeries, ABCDatetimeIndex, ABCPeriod
+from pandas.core.dtypes.generic import ABCPeriod
 from pandas.core.tools.datetimes import to_datetime
 import pandas.core.common as com
 
@@ -288,25 +288,6 @@ def _repr_attrs(self):
     def name(self):
         return self.rule_code
 
-    def __add__(self, other):
-        if isinstance(other, (ABCDatetimeIndex, ABCSeries)):
-            return other + self
-        elif isinstance(other, ABCPeriod):
-            return other + self
-        try:
-            return self.apply(other)
-        except ApplyTypeError:
-            return NotImplemented
-
-    def __sub__(self, other):
-        if isinstance(other, datetime):
-            raise TypeError('Cannot subtract datetime from offset.')
-        elif type(other) == type(self):
-            return self.__class__(self.n - other.n, normalize=self.normalize,
-                                  **self.kwds)
-        else:  # pragma: no cover
-            return NotImplemented
-
     def rollback(self, dt):
         """Roll provided date backward to next offset only if not on offset"""
         dt = as_timestamp(dt)
@@ -2106,7 +2087,7 @@ def f(self, other):
     return f
 
 
-class Tick(SingleConstructorOffset):
+class Tick(liboffsets._Tick, SingleConstructorOffset):
     _inc = Timedelta(microseconds=1000)
     _prefix = 'undefined'
     _attributes = frozenset(['n', 'normalize'])