Homogeneous current states in thin films and Josephson current in superconducting microbridges are studied within the framework of a two-band Ginzburg–Landau theory. By solving the coupled system of equations for two order parameters the depairing current curves and Josephson current–phase relation are calculated for different values of phenomenological parameters γ and η. Coefficients γ and η describe the coupling of order parameters (proximity effect) and their gradients (drag effect), respectively. For definite parameter values the dependence of the current j on the superfluid momentum q contains local minima and corresponding bistable states. It is shown that a Josephson microbridge made from two-band superconductors can demonstrate π-junction behavior.