Homozygosity mapping is a powerful strategy for mapping rare recessive traits in children of consanguineous marriages. Practical applications of this strategy are currently limited by the inability of conventional linkage analysis software to compute, in reasonable time, multipoint LOD scores for pedigrees with inbreeding loops. We have developed a new algorithm for rapid multipoint likelihood calculations in small pedigrees, including those with inbreeding loops. The running time of the algorithm grows, at most, linearly with the number of loci considered simultaneously. The running time is not sensitive to the presence of inbreeding loops, missing genotype information, and highly polymorphic loci. We have incorporated this algorithm into a software package, MAPMAKER/HOMOZ, that allows very rapid multipoint mapping of disease genes in nuclear families, including homozygosity mapping. Multipoint analysis with dozens of markers can be carried out in minutes on a personal workstation.