In this paper, we address some of the statistical issues concerning false-positive rates that arise when the whole genome, or a portion thereof, is scanned in distantly related individuals, to search for a disease locus. We derive a method for correcting false-positive probabilities for the large number of comparisons that are performed when scanning a large portion of the genome. We consider both the idealized situation of a dense set of fully informative markers and the more realistic data-collection strategy of an initial scan at low resolution to identify promising areas, which then are typed with markers at high resolution. We also examine the accuracy of false-positive rates approximated using a conservative estimate of the separation distance between affected individuals in the current generation and the common ancestral couple. Calculation of false-positive rates when inbreeding is present in the pedigree also is considered.