In this paper, the peristaltic flow of rheologically complex physiological fluids when modelled by a non-Newtonian Casson fluid in a two-dimensional channel is considered. Of interest is the difference between peristaltic transport of Newtonian and non-Newtonian fluids. A perturbation series method of solution of the stream function in amplitude ratio is sought. It is found that Newtonian fluid is an important sub-class of non-Newtonian fluids that may adequately represent some physiological phenomena. It is shown that for a Casson fluid, when certain simplifications and approximations are made in the most generalised form of constitutive equation, the fluid may be adequately represented as an improvement of a Newtonian fluid.