Back propagation neural networks is a new technology useful for modeling nonlinear functions of several variables. This paper explores their applications in the field of quantitative structure-activity relationships. In particular, their ability to fit biological activity surfaces, predict activity, and determine the "functional forms" of its dependence on physical properties is compared to well-established methods in the field. A dataset of 256 5-phenyl-3,4-diamino-6,6-dimethyldihydrotriazines that inhibit dihydrofolate reductase enzyme is used as a basis for comparison. It is found that neural networks lead to enhanced surface fits and predictions relative to standard regression methods. Moreover, they circumvent the need for ad hoc indicator variables, which account for a significant part of the variance in linear regression models. Additionally, they lead to the elucidation of nonlinear and "cross-products" effects that correspond to trade-offs between physical properties in their effect on biological activity. This is the first demonstration of the latter two findings. On the other hand, due to the complexity of the resulting models, an understanding of the local, but not the global, structure-activity relationships is possible. The latter must await further developments. Furthermore, the longer computational time required to train the networks is somewhat inconveniencing, although not restrictive.