I study the long-term behavior of populations of nonlinear oscillators with all-to-all, noninstantaneous, pulse coupling. With fast enough excitatory coupling both the fully synchronized and the asynchronous state are unstable. In this case individual units fire quasiperiodically even though the network as a whole shows a periodic finding pattern. The behavior of networks with three or more units is different in this regard from that of two-unit networks. With inhibitory coupling the network can break up into a variable number of fully synchronized clusters. For fast inhibition the number of clusters tends to be large, while the number of clusters is smaller for slow inhibition.
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