We study the time‐dependent compressible flow of a Newtonian fluid in slits using an arbitrary nonlinear slip law relating the shear stress to the velocity at the wall. This slip law exhibits a maximum and a minimum and so does the flow curve. According to one‐dimensional stability analyses, the steady‐state solutions are unstable if the slope of the flow curve is negative. The two‐dimensional flow problem is solved using finite elements for the space discretization and a standard fully implicit scheme for the time discretization. When compressibility is taken into account and the volumetric flow rate at the inlet is in the unstable regime, we obtain self‐sustained oscillations of the pressure drop and of the mass flow rate at the exit, similar to those observed with the stick‐slip instability. The effects of compressibility and of the length of the slit on the amplitude and the frequency of the oscillations are also examined.