In this paper we propose a robust version of Cox-type test statistics for the choice between two non-nested hypotheses. We first show that the influence of small amounts of contamination in the data on the test decision can be very large. Secondly we build a robust test statistic by using the results on robust parametric tests available in the literature and show that the level of the robust test is stable. Finally, we show numerically not only the good property of robustness of this new test statistic, but also that its asymptotic distribution is a good approximation of its sample distribution, unlike for the classical test statistic.