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Some examples of flows with separation zones and movable contact discontinuities obtained as a result of the numerical integration of the time-dependent equations for an ideal gas are presented. The examples concern a steady annular separation zone on the blunt nose of a body in a supersonic flow, periodic shedding of unsteady discontinuities from a cylinder in a steady uniform subsonic flow with a supercritical Mach number, and the complicated deformation of a contact (tangential) discontinuity, namely, the boundaries of a two-dimensional jet, either subsonic or supersonic, flowing into a cocurrent subsonic low-velocity flow. A multiple increase in the difference grid capacity in the numerical integration of the Euler equations indicates the absence of a noticeable scheme viscosity effect in the examples calculated. The inviscid nature of the separation flows obtained is also confirmed by their well-known counterparts constructed in the ideal incompressible fluid approximation. The time-average velocity fields of the two-dimensional jet and the intensity of its sound field are in reasonable agreement with the available data.