diff --git a/brian2/core/clocks.py b/brian2/core/clocks.py
index 338b4f8bf..b1688a328 100644
--- a/brian2/core/clocks.py
+++ b/brian2/core/clocks.py
@@ -37,8 +37,7 @@ def check_dt(new_dt, old_dt, target_t):
     ------
     ValueError
         If using the new dt value would lead to a difference in the target
-        time of more than `Clock.epsilon_dt` times ``new_dt`` (by default,
-        0.01% of the new dt).
+        time of more than `Clock.epsilon_dt` (by default, 10ns).
 
     Examples
     --------
@@ -53,7 +52,7 @@ def check_dt(new_dt, old_dt, target_t):
     old_t = np.int64(np.round(target_t / old_dt)) * old_dt
     new_t = np.int64(np.round(target_t / new_dt)) * new_dt
     error_t = target_t
-    if abs(new_t - old_t)/new_dt > Clock.epsilon_dt:
+    if abs(new_t - old_t) > Clock.epsilon_dt:
         raise ValueError(('Cannot set dt from {old} to {new}, the '
                           'time {t} is not a multiple of '
                           '{new}').format(old=str(old_dt * second),
@@ -75,10 +74,8 @@ class Clock(VariableOwner):
     Notes
     -----
     Clocks are run in the same `Network.run` iteration if `~Clock.t` is the
-    same. The condition for two
-    clocks to be considered as having the same time is
-    ``abs(t1-t2)<epsilon*abs(t1)``, a standard test for equality of floating
-    point values. The value of ``epsilon`` is ``1e-14``.
+    same. The condition for two clocks to be considered as having the same time
+    is ``abs(t1-t2)<10*ns``.
     '''
 
     def __init__(self, dt, name='clock*'):
@@ -122,7 +119,7 @@ def _set_t_update_dt(self, target_t=0*second):
     def _calc_timestep(self, target_t):
         '''
         Calculate the integer time step for the target time. If it cannot be
-        exactly represented (up to 0.01% of dt), round up.
+        exactly represented (up to 10ns), round up.
 
         Parameters
         ----------
@@ -137,7 +134,7 @@ def _calc_timestep(self, target_t):
         new_i = np.int64(np.round(target_t / self.dt_))
         new_t = new_i * self.dt_
         if (new_t == target_t or
-                        np.abs(new_t - target_t)/self.dt_ <= Clock.epsilon_dt):
+                        np.abs(new_t - target_t) <= Clock.epsilon_dt):
             new_timestep = new_i
         else:
             new_timestep = np.int64(np.ceil(target_t / self.dt_))
@@ -190,9 +187,9 @@ def set_interval(self, start, end):
                                      self._i_end),
                         'many_timesteps')
 
-    #: The relative difference for times (in terms of dt) so that they are
+    #: The absolute difference for times (in seconds) so that clocks are
     #: considered identical.
-    epsilon_dt = 1e-4
+    epsilon_dt = 1e-8
 
 
 class DefaultClockProxy(object):
diff --git a/brian2/core/network.py b/brian2/core/network.py
index 649fece2a..0d49a1d5a 100644
--- a/brian2/core/network.py
+++ b/brian2/core/network.py
@@ -933,7 +933,7 @@ def _nextclocks(self):
         minclock, min_time, minclock_dt = min(clocks_times_dt, key=lambda k: k[1])
         curclocks = {clock for clock, time, dt in clocks_times_dt if
                         (time == min_time or
-                         abs(time - min_time)/min(minclock_dt, dt) < Clock.epsilon_dt)}
+                         abs(time - min_time) < Clock.epsilon_dt)}
         return minclock, curclocks
 
     @device_override('network_run')
diff --git a/brian2/tests/test_clocks.py b/brian2/tests/test_clocks.py
index b3b12bbd2..359f6aba1 100644
--- a/brian2/tests/test_clocks.py
+++ b/brian2/tests/test_clocks.py
@@ -44,6 +44,7 @@ def test_defaultclock():
     assert_equal(defaultclock.dt, 1*ms)
     assert defaultclock.name == 'defaultclock'
 
+
 @pytest.mark.codegen_independent
 def test_set_interval_warning():
     clock = Clock(dt=0.1*ms)
@@ -56,6 +57,31 @@ def test_set_interval_warning():
     assert logs[0][1].endswith('many_timesteps')
 
 
+@pytest.mark.codegen_independent
+def test_very_long_dt():
+    # See github issue #1054
+    clock1 = Clock(dt=0.1*ms)
+    clock2 = Clock(dt=100000*second)
+    clock1.set_interval(0*ms, 1*ms)
+    clock2.set_interval(0*ms, 1*ms)  # The clock should advance
+    assert clock1.timestep[:] == 0
+    assert clock2.timestep[:] == 0
+    assert clock1._i_end == 10
+    assert clock2._i_end == 1
+    # Simulate advancing the clock
+    clock1.variables['timestep'].set_value(clock1._i_end)
+    clock1.variables['t'].set_value(clock1._i_end * clock1.dt)
+    clock2.variables['timestep'].set_value(clock2._i_end)
+    clock2.variables['t'].set_value(clock2._i_end * clock2.dt)
+
+    clock1.set_interval(1*ms, 2*ms)
+    clock2.set_interval(1*ms, 2*ms)  # The clock should not advance
+    assert clock1.timestep[:] == 10
+    assert clock2.timestep[:] == 1
+    assert clock1._i_end == 20
+    assert clock2._i_end == 1
+
+
 if __name__ == '__main__':
     test_clock_attributes()
     restore_initial_state()
@@ -63,3 +89,4 @@ def test_set_interval_warning():
     restore_initial_state()
     test_defaultclock()
     test_set_interval_warning()
+    test_very_long_dt()