Interest in equivalence trials has been increasing for many years, though the methodology which has been developed for such trials is mainly for uncensored data. In cancer research we are more often concerned with survival. In an efficacy trial, the null hypothesis specifies equality of the two survival distributions, but in an equivalence trial, a null hypothesis of inequivalence H0 has to be tested. The usual logrank test has to be modified to test whether the true value r of the ratio of hazard rates in two treatment groups is at least equal to a limit value r0. If prognostic factors have to be taken into account, the Cox model provides tests of Ho, and a useful confidence interval for the adjusted relative derived from the regression parameter for the treatment indicator. An equivalence trial of maintenance therapy was carried out in children with B non-Hodgkin lymphoma, and serves as an illustration.