A product unit is a formal neuron that multiplies its input values instead of summing them. Furthermore, it has weights acting as exponents instead of being factors. We investigate the complexity of learning for networks containing product units. We establish bounds on the Vapnik-Chervonenkis (V-C) dimension that can be used to assess the generalization capabilities of these networks. In particular, we show that the VC dimension for these networks is not larger than the best known bound for sigmoidal networks. For higher-order networks, we derive upper bounds that are independent of the degree of these networks. We also contrast these results with lower bounds.