Using a probabilistic approach, the parallel dynamics of the Q-state Potts and Q-Ising neural networks are studied at zero and at nonzero temperatures. Evolution equations are derived for the first time step and arbitrary Q. These formulas constitute recursion relations for the exact parallel dynamics of the extremely diluted asymmetric versions of these networks. An explicit analysis, including dynamical capacity-temperature diagrams and the temperature dependence of the overlap, is carried out for Q = 3. Both types of models are compared.