We investigate the behavior of a Hebbian cell assembly of spiking neurons formed via a temporal synaptic learning curve. This learning function is based on recent experimental findings. It includes potentiation for short time delays between pre-and post-synaptic neuronal spiking, and depression for spiking events occuring in the reverse order. The coupling between the dynamics of the synaptic learning and of the neuronal activation leads to interesting results. We find that the cell assembly can fire asynchronously, but may also function in complete synchrony, or in distributed synchrony. The latter implies spontaneous division of the Hebbian cell assembly into groups of cells that fire in a cyclic manner. We invetigate the behavior of distributed synchrony both by simulations and by analytic calculations of the resulting synaptic distributions.