The recent discovery of hypervariable VNTR (variable number of tandem repeat) loci has led to much excitement among population biologists regarding the feasibility of deriving individual estimates of relatedness in field populations by DNA fingerprinting. It is shown that unbiased estimates of relatedness cannot be obtained at the individual level without knowledge of the allelic distributions in both the individuals of interest and the base population unless the proportion of shared marker alleles between unrelated individuals is essentially zero. Since the latter is usually on the order of 0.1-0.5 and since there are enormous practical difficulties in obtaining the former, only an approximate estimator for the relatedness can be given. The bias of this estimator is individual specific and inversely related to the number of marker loci and frequencies of marker alleles. Substantial sampling variance in estimates of relatedness arises from variation in identity by descent within and between loci and, with finite numbers of alleles, from variation in identity in state between genes that are not identical by descent. In the extreme case of 25 assayed loci, each with an effectively infinite number of alleles, the standard error of a relatedness estimate is no less than 14%, 20%, 35%, and 53% of the expectation for full sibs and second-, third-, and fourth-order relationships, respectively. Attempts to ascertain relatedness by means of DNA fingerprinting should proceed with caution.