diff --git a/sympy/core/basic.py b/sympy/core/basic.py
index 46ae7264a19..d5007133b71 100644
--- a/sympy/core/basic.py
+++ b/sympy/core/basic.py
@@ -41,7 +41,8 @@ class Basic(metaclass=ManagedProperties):
     """
     __slots__ = ['_mhash',              # hash value
                  '_args',               # arguments
-                 '_assumptions'
+                 '_assumptions',
+                 '__weakref__'
                 ]
 
     # To be overridden with True in the appropriate subclasses
diff --git a/sympy/core/cache.py b/sympy/core/cache.py
index 7c5cc7dbe23..aa3f178256d 100644
--- a/sympy/core/cache.py
+++ b/sympy/core/cache.py
@@ -1,6 +1,7 @@
 """ Caching facility for SymPy """
 
 from decorator import decorator
+import weakref
 
 
 # TODO: refactor CACHE & friends into class?
@@ -81,7 +82,7 @@ def __cacheit(f):
     set environment variable SYMPY_USE_CACHE to 'debug'.
     """
 
-    func_cache_it_cache = {}
+    f._cache_it_cache = func_cache_it_cache = weakref.WeakValueDictionary()
     CACHE.append((f, func_cache_it_cache))
 
     def wrapper(f, *args, **kw_args):
diff --git a/sympy/core/tests/test_symbol.py b/sympy/core/tests/test_symbol.py
index 8e57fad04b0..0badf8300aa 100644
--- a/sympy/core/tests/test_symbol.py
+++ b/sympy/core/tests/test_symbol.py
@@ -1,8 +1,11 @@
+import gc
+import weakref
+
 import pytest
 
 from sympy import (Symbol, Wild, GreaterThan, LessThan, StrictGreaterThan,
                    StrictLessThan, pi, I, Rational, sympify, symbols, Dummy,
-                   Integer, Float, sstr)
+                   Integer, Float, sstr, default_sort_key)
 
 
 def test_Symbol():
@@ -332,3 +335,12 @@ def test_call():
     f = Symbol('f')
     assert f(2)
     pytest.raises(TypeError, lambda: Wild('x')(1))
+
+
+def test_weakref():
+    x, y = Symbol('x'), Symbol('y')
+    d = weakref.WeakKeyDictionary([(x, 1), (y, 2)])
+    assert sstr(sorted(d.keys(), key=default_sort_key)) == '[x, y]'
+    del x
+    gc.collect()
+    assert sstr(list(d.keys())) == '[y]'
diff --git a/sympy/utilities/tests/test_pickling.py b/sympy/utilities/tests/test_pickling.py
index 5fcfbc8d640..3afc093c609 100644
--- a/sympy/utilities/tests/test_pickling.py
+++ b/sympy/utilities/tests/test_pickling.py
@@ -24,7 +24,7 @@
 
 from sympy import symbols, S
 
-excluded_attrs = {'_assumptions', '_mhash'}
+excluded_attrs = {'_assumptions', '_mhash', '__weakref__'}
 
 
 def check(a, exclude=[], check_attr=True):