In this paper we present and compare three different massively parallel implementations of multilayer feedforward neural networks on a MasPar MP-1216, a parallel SIMD computer with 16,384 processors. For multilayer feedforward networks we have obtained sustained rates of up to 348 MCPS and 129 MCUPS with backpropagation, a high mark for general purpose SIMD computers. After a brief introduction to SNNS, the paper first focuses on the problems of mapping neural networks to parallel hardware. Different aspects of parallelism are presented. Two combinations of unit and training pattern parallelism were implemented as well as link and training pattern parallelism. We describe the implementation problems in obtaining high propagation rates on a SIMD machine and problems with the resulting learning algorithms in general.