Relatedness between individuals is an important element of genetic-epidemiological and evolutionary investigations in the context of anthropological research. In general, data on relationships between individuals are gathered from personal interviews or from examination of vital records. When blood samples are collected, such information can be validated from genotypic similarities of individuals. Although genotype data may offer opportunities to exclude certain types of relationships, inclusionary statements are necessarily only probabilistic in nature. The limitations of such probabilistic statements depend on the number of segregating alleles and the extent of polymorphisms at the loci employed. With the advent of DNA technology, several hypervariable single-locus probes (SLPs) and multilocus probes (MLPs) are now available for many organisms. These can be used to circumvent limitations of unequivocal assignment of relationships from genotype data. In this article we describe analytical principles for such investigations. In particular, we propose summary measures of DNA fingerprinting data (e.g., number of different alleles and number of shared alleles) that can be used to describe kinship relationships between individuals. We derive the expected distributions of number of alleles in individuals and of number of shared alleles between individuals of known relationships in a population. These distributions can be used in hypothesis testing to determine relatedness between individuals. We also derive the number of SLPs, each detecting a hypervariable polymorphism, needed to determine a specified relationship for given ranges of errors of prediction. Illustrations of the theory with data on several short tandem repeat loci and variable number of tandem repeat (VNTR) loci indicate that with 6 to 12 SLPs the parent-offspring pairs can be reliably distinguished from random pairs of individuals. This theory also serves the purpose of detecting inbreeding levels in a natural population.