Some optimum nonparametric tests and estimates for contrasts of interactions in two-factor models with replications are proposed and discussed. These procedures are based on nonparametric estimates of the type considered by Hodges and Lehmann [4]. Unbiasedness and joint asymptotic normality of the estimates are proved and the asymptotic efficiencies relative to the least squares procedure is found. It is shown that, in the special cases of Wilcoxon and normal scores, these methods are more robust than least squares against changes in the underlying distribution. Also, confidence intervals based on the above procedures are investigated (c.f. [12]). An example is given to explain the computations.