This paper presents a study of the Fuzzy ARTMAP neural network in designing cascaded gratings and Frequency Selective Surfaces (FSS) in general. Conventionally, trial-and-error procedures are used until an FSS matches the design criteria. One way of avoiding this laborious and manual process is to use neural networks. A neural network can be trained to predict the dimensions of the metallic patches (or apertures), their distance of separation, their shape, and the number of layers required in a multilayer structure which gives the desired frequency response. In the past, to achieve this goal, the backpropagation (backprop) learning algorithm was used in conjunction with an inversion algorithm. Unfortunately, the backprop algorithm sometimes has problems with convergence. In this work the Fuzzy ARTMAP neural networks is utilized. The Fuzzy ARTMAP is faster to train than the backprop and it does not require an inversion algorithm to solve the FSS problem. Most importantly, its convergence is guaranteed. Several results (frequency responses) from cascaded gratings for various angles of wave incidence, layer separation, width strips, and interstrip separation are presented and discussed.