  We analyze two pulse-coupled resonate-and-fire neurons. Numerical simulation
reveals that an anti-phase state is an attractor of this model. We can
analytically explain the stability of anti-phase states by means of a return
map of firing times, which we propose in this paper. The resultant stability
condition turns out to be quite simple. The phase diagram based on our theory
shows that there are two types of anti-phase states. One of these cannot be
seen in coupled integrate-and-fire models and is peculiar to resonate-and-fire
models. The results of our theory coincide with those of numerical simulations.
