diff --git a/CHANGELOG.md b/CHANGELOG.md
index b3f3868e..aedcc7ea 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -28,6 +28,8 @@
 
 - fix: optimizer doesn't recurse into And/Or/Some children @williballenthin #3020
 
+- fix: address classes __eq__ and __lt__ assert on type @williballenthin #3021
+
 ### capa Explorer Web
 
 ### capa Explorer IDA Pro plugin
diff --git a/capa/features/address.py b/capa/features/address.py
index 95e4ba64..110c2816 100644
--- a/capa/features/address.py
+++ b/capa/features/address.py
@@ -68,11 +68,13 @@ class ProcessAddress(Address):
         return hash((self.ppid, self.pid))
 
     def __eq__(self, other):
-        assert isinstance(other, ProcessAddress)
+        if not isinstance(other, ProcessAddress):
+            return NotImplemented
         return (self.ppid, self.pid) == (other.ppid, other.pid)
 
     def __lt__(self, other):
-        assert isinstance(other, ProcessAddress)
+        if not isinstance(other, ProcessAddress):
+            return NotImplemented
         return (self.ppid, self.pid) < (other.ppid, other.pid)
 
 
@@ -91,11 +93,13 @@ class ThreadAddress(Address):
         return hash((self.process, self.tid))
 
     def __eq__(self, other):
-        assert isinstance(other, ThreadAddress)
+        if not isinstance(other, ThreadAddress):
+            return NotImplemented
         return (self.process, self.tid) == (other.process, other.tid)
 
     def __lt__(self, other):
-        assert isinstance(other, ThreadAddress)
+        if not isinstance(other, ThreadAddress):
+            return NotImplemented
         return (self.process, self.tid) < (other.process, other.tid)
 
 
@@ -114,10 +118,13 @@ class DynamicCallAddress(Address):
         return hash((self.thread, self.id))
 
     def __eq__(self, other):
-        return isinstance(other, DynamicCallAddress) and (self.thread, self.id) == (other.thread, other.id)
+        if not isinstance(other, DynamicCallAddress):
+            return NotImplemented
+        return (self.thread, self.id) == (other.thread, other.id)
 
     def __lt__(self, other):
-        assert isinstance(other, DynamicCallAddress)
+        if not isinstance(other, DynamicCallAddress):
+            return NotImplemented
         return (self.thread, self.id) < (other.thread, other.id)
 
 
diff --git a/tests/test_engine.py b/tests/test_engine.py
index 3d5e0a6d..d3f78488 100644
--- a/tests/test_engine.py
+++ b/tests/test_engine.py
@@ -12,9 +12,12 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+import pytest
+
 import capa.features.address
 from capa.engine import Or, And, Not, Some, Range
 from capa.features.insn import Number
+from capa.features.address import ThreadAddress, ProcessAddress, DynamicCallAddress
 
 ADDR1 = capa.features.address.AbsoluteVirtualAddress(0x401001)
 ADDR2 = capa.features.address.AbsoluteVirtualAddress(0x401002)
@@ -194,3 +197,52 @@ def test_eval_order():
 
     assert Or([Number(1), Number(2)]).evaluate({Number(2): {ADDR1}}).children[1].statement == Number(2)
     assert Or([Number(1), Number(2)]).evaluate({Number(2): {ADDR1}}).children[1].statement != Number(1)
+
+
+def test_address_cross_type_eq():
+    proc = ProcessAddress(pid=1, ppid=0)
+    ava = capa.features.address.AbsoluteVirtualAddress(0x401001)
+
+    assert (proc == ava) is False
+    assert (ava == proc) is False
+
+
+def test_process_address_sorting():
+    proc1 = ProcessAddress(pid=1, ppid=0)
+    proc2 = ProcessAddress(pid=2, ppid=0)
+
+    assert sorted([proc2, proc1]) == [proc1, proc2]
+
+
+def test_process_address_cross_type_sort_raises():
+    proc = ProcessAddress(pid=1, ppid=0)
+    ava = capa.features.address.AbsoluteVirtualAddress(0x401001)
+
+    with pytest.raises(TypeError):
+        sorted([proc, ava])
+
+
+def test_process_address_lt_returns_not_implemented_for_other_types():
+    proc = ProcessAddress(pid=1, ppid=0)
+    ava = capa.features.address.AbsoluteVirtualAddress(0x401001)
+
+    assert proc.__lt__(ava) is NotImplemented
+
+
+def test_thread_address_cross_type_eq():
+    proc = ProcessAddress(pid=1, ppid=0)
+    thread = ThreadAddress(process=proc, tid=10)
+    ava = capa.features.address.AbsoluteVirtualAddress(0x401001)
+
+    assert (thread == ava) is False
+    assert (ava == thread) is False
+
+
+def test_dynamic_call_address_cross_type_eq():
+    proc = ProcessAddress(pid=1, ppid=0)
+    thread = ThreadAddress(process=proc, tid=10)
+    call = DynamicCallAddress(thread=thread, id=0)
+    ava = capa.features.address.AbsoluteVirtualAddress(0x401001)
+
+    assert (call == ava) is False
+    assert (ava == call) is False