This report concerns likelihood ratio tests in a heterogeneous model for linkage, where the recombination fraction has a binomial mixture distribution with an unknown proportion of unlinked families. We consider families of unequal sizes with known or unknown phase data. In both cases, the limit distributions of the linkage test statistics are a mixture of a mass at ) and of a X2/1 distribution in equal proportions and homogeneity test statistics tend to the supremum of Gaussian processes. The critical values of the homogeneity tests are simulated, and the power functions of the linkage and homogeneity tests are compared in a simulation study.