We address the problem of the convergence to equilibrium of a
general class of point processes, containing, in particular, the nonlinear
mutually exciting point processes, an extension of the linear Hawkes processes,
and give general conditions guaranteeing the existence of a stationary version
and the convergence to equilibrium of a nonstationary version, both in
distribution and in variation. We also give a new proof of a result of Kerstan
concerning point processes with bounded intensity and general nonlinear
dynamics satisfying a Lipschitz condition.