Model-free methods of testing for association of a disease with alleles at a marker locus were used to analyze simulated data for a rare disease locus and 360 marker loci distributed at 2 cM intervals along six chromosomes. After adjustment for multiple tests, there was no evidence of significant heterogeneity of parental allele frequencies between a sample of parents with at least one affected child and a sample of parents with no affected children. Several significant deviations from Hardy-Weinberg equilibrium were detected after Bonferroni correction but these were Type I errors. After adjusting for multiple tests, the model-free test for association detected significant associations of alleles at two loci with the disease. These associations were in fact part of the generating model for the simulated data. However, these methods were unable to detect two other major loci contributing to the disease since these loci were not associated with any of the marker loci. ©1995 Wiley-Liss, Inc.