We have performed a number of one-dimensional hybrid simulations (massless electrons, macroions) of almost parallel collisionless shocks (angle between the upstream magnetic field and shock normal of 5¿) for medium and high Mach number shocks. One of the key questions we address is whether downstream convected upstream waves or waves locally generated at the interface of the incoming solar wind and the partially thermalized plasma are the main source of the downstream turbulence. In the medium, supercritical Mach number regime the small-wavelength interface waves are damped in a transition region and contribute to downstream dissipation [Krauss-Varban, 1995>. These waves are right-hand polarized and propagate in the downstream rest frame toward the shock. In an Alfv¿n Mach number regime around MA~8 we find behind the shock ramp right-hand polarized waves with both helicities. These are interpreted in terms of both the ion/ion resonant and the ion/ion right-hand nonresonant instability occurring in the shock transition region. The latter occurs, according to linear theory, when the beam density is high and when the relative speed between the ion beam and the ambient ions is large. In this Mach number regime the shock-produced waves have larger wavelengths and are less strongly damped. We suggest that they are subject to a parametric decay instability, resulting in an inverse cascade of short-wavelength waves to longer ones farther downstream. In the very high Mach number regime, damping as well as decay of the shock-produced waves is slow in comparison with the transit time from the shock to the magnetopause. The shock-generated waves are then the dominant source of the downstream turbulence.¿ 1997 American Geophysical Union