The gasdynamic problem of collapsing shocks and detonation waves having spherical or cylindrical symmetry is considered near the point or axis of symmetry. The solution basic to this work is the self-similar flow of a collopsing symmetrical shock wave with counterpressure neglected. The focusing effect as the flow progresses causes the front to accelerate and its velocity is singular at the instant of collapse. In the present work the perturbations, due to counter-pressure and also to a uniform heat release, which give rise to essentially identical mathematical solutions, are evaluated. The basic self-similar solution is investigated in detail over a range of values of the specific heat ratio.