In this paper our recently introduced method called output distributional influence function (ODIF) is used for the evaluation of the robustness properties of the nonlinear filter class of morphological filters. Several examples of the ODIFs for the dilation, closing and clos-opening are given and explained carefully. For each of these morphological filters the effect of filter length is examined by using the ODIFs for the expectation and variance. The robustness properties of the filters are also compared to each other and the effect of the distribution of the contamination is investigated for the closing as an example of realistic filtering conditions.