Semi-parametric regression models assume that the effects of covariates on the mean response are additive. We propose a test of additivity when there is one continuous covariate and a group indicator. At p fixed points, the differences of the within-group kernel estimates of the means are calculated, and the likelihood ratio test that the p differences have a constant mean is formed. The kernel bandwidth and the location of the p fixed points are chosen to give the test good power. Performance of the proposed test is compared with parametric and non-parametric tests of additivity. Published in 2001 by John Wiley & Sons, Ltd.