This paper presents analysis, computer modeling and experimental measurements of the photoconductive decay which occurs on cessation of illumination, in amorphous semiconductors. We explore the processes of relaxation of the excess carrier distributions using a capture-rate analysis, and examine the relative roles of re-trapping and recombination in exemplar cases of exponential trapping state profiles, with monomolecular and bimolecular recombination. We classify decay under strong or weak retrapping conditions which can be selected for by the prior steady generation rate, and this results in a rich variety of possible decay behavior. We examine several plausible intuitive explanations of the decay process, and show in detail that these explanations fail to predict accurately the speed and generation rate dependence of the decay. Results of experimental measurements of the decay from steady state and the impulse response in films of a-Si 1-x C x :H are presented.