We present analysis, computer modelling 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, and examine the relative rôles of re-trapping and recombination in a model case of an exponential trapping state profile, with monomolecular recombination. A variety of possible decay behaviour is revealed. We examine several plausible intuitive explanations of the decay process, including (a) the assumption that the rate limiting step in the decay process is the thermal release of trapped carriers from the vicinity of the quasi - Fermi level, and (b) multiple re-trapping at the quasi -Fermi level prior to recombination. Actual decay rates, however are often much faster than that predicted by these assumptions, and the generation rate dependencies do not follow the relation expected. These explanations are shown in detail to be largely erroneous. Results of experimental measurements of the decay from steady state and TPC in films of a-Si1-xCx:H are presented. While these appear initially to be at variance with the predictions of the present work, we demonstrate that the observations can be reconciled fully with theory.