  The counterflow transport in quantum Hall bilayers provided by superfluid
excitons is locked at small input currents due to a complete leakage caused by
the interlayer tunneling. We show that the counterflow critical current
I_c^{CF} above which the system unlocks for the counterflow transport can be
controlled by a tilt of magnetic field in the plane perpendicular to the
current direction. The effect is asymmetric with respect to the tilting angle.
The unlocking is accompanied by switching of the systems from the d.c. to the
a.c. Josephson state. Similar switching takes place for the tunneling set-up
when the current flowing through the system exceeds the critical value I_c^T.
At zero tilt the relation between the tunnel and counterflow critical currents
is I_c^T=2 I_c^{CF}. We compare the influence of the in-plane magnetic field
component B_\parallel on the critical currents I_c^{CF} and I_c^T. The in-plane
magnetic field reduces the tunnel critical current and this reduction is
symmetric with respect to the tilting angle. It is shown that the difference
between I_c^{CF} and I_c^T is essential at field |B_\parallel|\lesssim \phi_0/d
\lambda_J, where \phi_0 is the flux quantum, d is the interlayer distance, and
\lambda_J is the Josephson length. At larger B_\parallel the critical currents
I_c^{CF} and I_c^T almost coincide each other.
