Stationary waves in a superfluid magnetoexciton gas inν = 1 quantum Hall bilayers are considered. The waves are induced by counterpropagatingelectrical currents that flow in a system with a point obstacle. It is shown that stationarywaves can emerge only in imbalanced bilayers in a certain diapason of currents.It is found that the stationary wave pattern is modified qualitatively under avariation of the ratio of the interlayer distance to the magnetic length . The advantages of using graphene–dielectric–graphene sandwiches for the observation ofstationary waves are discussed. We determine the range of parameters (the dielectricconstant of the layer that separates two graphene layers and the ratio ) for which the state with superfluid magnetoexcitons can be realized in such sandwiches.Typical stationary wave patterns are presented as density plots.