Many phylogenetic analyses are inspired by or depend upon the monophyly of a group specified a priori. Also, many evolutionary problems for which phytogenies are useful do not require every detail of the phylogeny to be estimated correctly but depend upon the monophyly (or lack thereof) of a particular group. We propose a likelihood-ratio test that compares whether the best trees estimated with and without the constraint of monophyly are significantly different. Simulation suggests that the test is conservative when the null hypothesis (a particular specified constraint) is correct. We applied the likelihood-ratio test of monophyly to the question of the relationship of the presumed-extinct marsupial wolf (Thyladnus). Specifically, we examined the null hypotheses that (1) the marsupial wolf does not form a monophyletic group with dasyurids and (2) the marsupial wolf is a basal member of the Australian radiation of mammals. Both hypotheses were rejected using the likelihood-ratio test of monophyly. (Likelihood-ratio test; max- imum likelihood; monophyly; phylogenetic methods; Thylacinus.)