We describe a class of nonparametric tests for linkage between a marker and a gene assumed to exist and to govern susceptibility to a disease. The tests are formed by assigning a score to each possible pattern of marker allele sharing (identity-by-descent) among affected pedigree members, and then averaging the scores over all patterns compatible with the observed marker genotype and genealogical relationship of the affected members. Different score functions give different tests. One function, which examines marker allele similarity across pairs of affected pedigree members, gives a test similar to that of Fimmers et al. (1989, in Multipoint Mapping and Linkage Based on Affected Pedigree Members: Genetic Analysis Workshop, R. C. Elston, M. A. Spence, S. E. Hodge, and J. W. MacCluer (eds), 123-128; City: Alan R. Liss). A second function examines allele similarity across arbitrary subsets, not just pairs, of affected members. The resulting test can be more powerful than the one based solely on pairs of affected members. The approach has several advantages: it does not require knowledge of the mode of disease inheritance; it does not require unambiguous determination of identity-by-descent at the marker; it does not suffer from variability due to chance allele similarity among affected members who are unrelated, such as spouses; it allows marker genotypes of unaffected members to contribute information on allele sharing among the affected; it permits calculation of exact P-values. Computational requirements limit the tests to many pedigrees with few (<16) affected members.