In the paper of Rocha et al., J Optim Theory Appl (2016) 171:964979, the authors introduced a proximal point algorithm with quasi-distances to solve unconstrained convex multi-objective minimization problems. They proved that all accumulation points are ecient solutions of the problem. In this pa- per we analyze an inexact proximal point algorithm to solve convex and qua- siconvex unconstrained multi-objective minimization problems using quasi- distances. For the convex case, we extend the result obtained by the exact algorithm of Rocha et al. and for the quasiconvex case we prove that all ac- cumulation points are Pareto-Clarke critical points of the problem. Finally, to show the practicality of the introduced algorithm, we present numerical examples that con rm the convergence of our algorithm.