Analysis of correlated spike trains is a hot topic of research in computational neuroscience. A general model of probability distributions for spikes includes too many parameters to be of use in analyzing real data. Instead, we need a simple but powerful generative model for correlated spikes. We developed a class of conditional mixture models that includes a number of existing models and analyzed its capabilities and limitations. We apply the model to dynamical aspects of neuron pools. When Hebbian cell assemblies coexist in a pool of neurons, the condition is specified by these assemblies such that the probability distribution of spikes is a mixture of those of the component assemblies. The probabilities of activation of the Hebbian assemblies change dynamically. We used this model as a basis for a competitive model governing the states of assemblies.