The interaction between collisionless shocks, such as arises in the distant solar wind as well as other situations in space plasmas, is examined by means of hybrid numerical simulations. It is shown that the collision between two perpendicular collisionless shocks gives rise to a tangential discontinuity located between the two transmitted shocks, as predicted by MHD theory. The discontinuity has a clear jump in the density, temperature and magnetic field strength. The width of the discontinuity is found to be a few (1--4) ion Larmor radii. The collision between two oblique shocks produces a much more extensive and turbulent region between the two transmitted shocks and it is suggested that this may be a contact discontinuity. The contact discontinuity also shows jumps in the plasma and magnetic field components and has a helical magnetic field structure. The widths of these discontinuities are narrower than those typically observed in the inner solar wind. ¿ American Geophysical Union 1990