When postsynaptic conductance varies slowly compared to the spike generation process, a straightforward averaging scheme can be used to reduce the system's complexity. Our model consists of a Hodgkin-Huxley-like membrane description for each cell; synaptic activation is described by first order kinetics, with slow rates, in which the equilibrium activation is a sigmoidal function of the presynaptic voltage. Our work concentrates on a two-cell network and it applies qualitatively to the activity patterns, including bistable behavior, recently observed in simple in vitro circuits with slow synapses (Kleinfeld et al . 1990). The fact that our averaged system is derived from a realistic biophysical model has important consequences. In particular, it can preserve certain hysteresis behavior near threshold that is not represented in a simple ad hoc sigmoidal input-output network. This behavior enables a coupled pair of cells, one excitatory and one inhibitory, to generate an alternating burst rhythm even though neither cell has fatiguing properties.