Context. The heliospheric current sheet is a plasma layer dividing the heliosphere into the regions of different magnetic field polarity. Since it is very thin compared to the size of the system, it is difficult to incorporate into the numerical models of the heliosphere. Because of the solar magnetic field reversals and the diverging and slowing down plasma flow in the outer heliosphere, the heliospheric current sheet is expected to have a complicated structure, with important consequences for transport processes in the heliosheath. Aims. We determine the shape and time evolution of the current sheet in selected time-dependent 3-D models of the heliosphere, assuming that the heliospheric current sheet is a tangential discontinuity convected by the plasma flow. Methods. We have derived the shape of the heliospheric current sheet at a given time by following the plasma flow lines originating at the neutral line on the source surface surrounding the Sun. The plasma flow was obtained from numerical MHD or gas-dynamical solutions.Results. The large-scale structure of the magnetic field polarity regions and the heliospheric current sheet in time-dependent asymmetric models of the heliosphere differs from the results obtained in simpler models. In particular, in the forward heliosheath it is characterized by secondary folds in the heliospheric current sheet that are caused by the solar wind latitudinal variation over the solar cycle. We present examples illustrating some cases of interest: a "bent" current sheet, and the HCS structure during the magnetic field reversal at the solar maximum. We also discuss the evolution of the magnetic polarity structure in the region close to the heliopause.