Many methods have been proposed for the stability analysis of systems described by non-linear differential equations. Of these methods, some are 'ad hoc', being applicable only to those systems for which they were developed. Others are more or less general. The increasing availability of digital computing facilities have made it desirable to develop algorithms, where possible, to allow the numerical implementation of these general methods. This report describes the development of such algorithms for a variety of methods, and a comparison of their power and applicability in different situations.