We consider some nonuniformly hyperbolic invertible dynamical system which are modeled by a Gibbs-Markov-Young tower.

We assume a polynomial tail for the inducing time and a polynomial control of hyperbolicity, as introduced by Alves, Pinheiro and Azevedo. These systems admit a physical measure with polynomial rate of mixing. In this paper we prove that the distribution of the successive entrances times into a ball $B(x,r)$ converges to a Poisson distribution as the radius $r\to0$ and after suitable normalization.