The present paper introduces a methodology for the semiparametric or non-parametric two-sample equivalence problem when the effects are specified by statistical functionals. The mean relative risk functional of two populations is given by the average of the time-dependent risk. This functional is a meaningful non-parametric quantity, which is invariant under strictly monotone transformations of the data. In the case of proportional hazard models, the functional determines just the proportional hazard risk factor. It is shown that an equivalence test of the type of the two-sample Savage rank test is appropriate for this functional. Under proportional hazards, this test can be carried out as an exact level α test. It also works quite well under other semiparametric models. Similar results are presented for a Wilcoxon rank-sum test for equivalence based on the Mann–Whitney functional given by the relative treatment effect.