diff --git a/python-distributed.changes b/python-distributed.changes
index 8c62b09..c183819 100644
--- a/python-distributed.changes
+++ b/python-distributed.changes
@@ -1,3 +1,11 @@
+-------------------------------------------------------------------
+Thu Dec  3 12:06:24 UTC 2020 - Markéta Machová <mmachova@suse.com>
+
+- Launch tests
+  * around 70 of them are inconsistently (sometimes they pass, sometimes 
+    fail) broken by new pytest-asyncio (and similar number of other tests 
+    got deselected mostly because of similar names)
+
 -------------------------------------------------------------------
 Sat Nov 21 22:35:43 UTC 2020 - Arun Persaud <arun@gmx.de>
 
diff --git a/python-distributed.spec b/python-distributed.spec
index 825a05e..0de55e4 100644
--- a/python-distributed.spec
+++ b/python-distributed.spec
@@ -18,8 +18,7 @@
 
 %define skip_python2 1
 %{?!python_module:%define python_module() python-%{**} python3-%{**}}
-# Test requires network connection
-%bcond_with     test
+%bcond_without     test
 Name:           python-distributed
 Version:        2.30.1
 Release:        0
@@ -36,32 +35,43 @@ BuildRequires:  python-rpm-macros
 Requires:       python-PyYAML
 Requires:       python-certifi
 Requires:       python-click >= 6.6
-Requires:       python-cloudpickle >= 1.3.0
-Requires:       python-contextvars
-Requires:       python-dask >= 2.7.0
+Requires:       python-cloudpickle >= 1.5.0
+Requires:       python-dask >= 2.9.0
 Requires:       python-joblib >= 0.10.2
 Requires:       python-msgpack
 Requires:       python-psutil >= 5.0
 Requires:       python-scikit-learn >= 0.17.1
 Requires:       python-sortedcontainers
 Requires:       python-tblib
-Requires:       python-toolz >= 0.7.4
+Requires:       python-toolz >= 0.8.2
+%if %{python_version_nodots} >= 38
+Requires:       python-tornado >= 6.0.3
+%else
+Requires:       python-contextvars
 Requires:       python-tornado >= 5
+%endif
 Requires:       python-zict >= 0.1.3
 BuildArch:      noarch
 %if %{with test}
 BuildRequires:  %{python_module PyYAML}
 BuildRequires:  %{python_module certifi}
 BuildRequires:  %{python_module click >= 6.6}
-BuildRequires:  %{python_module cloudpickle >= 1.3.0}
-BuildRequires:  %{python_module dask >= 0.18.0}
+BuildRequires:  %{python_module cloudpickle >= 1.5.0}
+BuildRequires:  %{python_module dask >= 2.9.0}
+BuildRequires:  %{python_module dask-bag >= 2.9.0}
+BuildRequires:  %{python_module dask-distributed >= 2.9.0}
 BuildRequires:  %{python_module msgpack}
 BuildRequires:  %{python_module psutil}
+BuildRequires:  %{python_module pytest-asyncio}
 BuildRequires:  %{python_module pytest}
 BuildRequires:  %{python_module sortedcontainers}
 BuildRequires:  %{python_module tblib}
-BuildRequires:  %{python_module toolz >= 0.7.4}
-BuildRequires:  %{python_module tornado >= 4.5.1}
+BuildRequires:  %{python_module toolz >= 0.8.2}
+%if %{python_version_nodots} >= 38
+BuildRequires:  %{python_module tornado >= 6.0.3}
+%else
+BuildRequires:  %{python_module tornado >= 5}
+%endif
 BuildRequires:  %{python_module zict >= 0.1.3}
 %endif
 %python_subpackages
@@ -86,7 +96,23 @@ clusters.
 
 %if %{with test}
 %check
-%pytest distributed/tests/
+# test_reconnect from test_client.py and all tests in test_core.py need network connection
+rm distributed/tests/test_core.py
+# many tests from multiple files are broken by new pytest-asyncio (see https://github.com/dask/distributed/pull/4212 for explanation)
+# as a proof build it with old pytest-asyncio and see these tests pass
+ASYNCIO_FAIL="test_worker_nthreads or test_identity or test_worker_port_range or test_worker_waits_for_scheduler or test_io_loop\
+ or test_deque_handler or test_bad_ or test_update_latency or test_heartbeat_comm_closed or test_get_client or test_lifetime\
+ or test_dashboard_link_ or test_shutdown or test_config or test_client_gather_semaphore_loop or test_secede_\
+ or test_event_on_workers or test_two_events_on_workers or test_lock or test_serializable or test_nanny_closes_cleanly or test_nanny_port_range\
+ or test_nanny_closed_by_keyboard_interrupt or test_worker_start_exception or test_2220 or test_config_stealing or test_async_context_manager\
+ or test_allowed_failures_config or test_no_danglng_asyncio_tasks or test_multiple_listeners or test_oversubscribing_leases\
+ or test_security_dict_input or test_worker_client or test_tls_scheduler or test_release_once_too_many_resilience or test_close_async\
+ or test_access_semaphore_by_name or test_release_simple or test_worker_breaks_and_returns or test_num_fds or test_retire_names_str or test_gather_allow_worker_reconnect"
+# test_worker_client.py and test_preload.py are also heavily affected by new asyncio, more than half of all tests there are broken
+rm distributed/tests/test_worker_client.py distributed/tests/test_preload.py
+# test_fail_write_to_disk randomly fails
+export PYTHONPATH=.
+%pytest distributed/tests/ -k "not (test_reconnect or $ASYNCIO_FAIL or test_fail_write_to_disk)"
 %endif
 
 %files %{python_files}