The problem of vector quantizing the parameters of a neural network is addressed, followed by a discussion of different algorithms applicable for quantizer design. Optimal, as well as several suboptimal quantization schemes are described. Simulations involving nonlinear prediction of speech signals are presented to compare the performance of different quantization techniques. Performance evaluation conducted uncover the tradeoffs in implementational complexity. Among the three examined suboptimal quantization schemes, it is shown that the multistage quantizer offers the best tradeoff between complexity and performance.