W. M. Schaffer's principal interests involve the application of nonlinear dynamics to biology at a variety of levels. At the biochemical level, he has collaborated with T. V. Bronnikova and others on the the peroxidase-oxidase reaction, which has become a model system for the study of complex dynamical behavior in a biochemical contexts. This work has resulted in the production of the first detailed model which is able to reproduce complicated bifurcation sequences observed in careful laboratory experiments. At the physiological level, he is interested in dynamical scenarios which might account for the natural history of diseases such as epilepsy in which the (overt manifestations) of the pathology are intermittent. This work is still preliminary. At the ecological level, he is concerned with complex population dynamics and with the ups and downs of human epidemics. His work on chaos in childhood diseases, in particular, sparked considerable interest in this topic. Presently, he is studying predator-prey dynamics in the presence of seasonality. This work has interesting mathematical content as well as implications for the control of insect pest species in agroecosystems.