Some large-sample properties of the three nonparametric tests of David and Fix for the two-sample bivariate location problem are given. In particular the Pitman A.R.E.s of the tests against some ‘normal-theory’ competitors are shown to be satisfactory in most cases for a number of ‘near-normal’ bivariate distributions. Their performances in some mixtures of bivariate normal distributions prove to be particularly convincing. A useful relationship between the three test statistics is indicated.