The need for simple and well understood mathematical models representative of the dynamics of large physical systems has long been recognised, and has recently attracted considerable attention. This work was prompted by previous studies in the department showing that the responses of complex models of absorption columns could be represented equally well by much simpler models. The study has covered three areas: (a) the reduction of order of transfer functions; (b) the reduction of order of state-variable models; (c) associated topics and numerical techniques. A survey has been carried out on methods for reducing state-variable models, or transfer functions, to lower order transfer functions. A number of schemes have been studied, including least-squares fitting in the frequency domain, the truncation of continued fractions, and the matching of moments. It has been shown that in certain situations the continued fraction and moments matching method are in fact identical.