Formulae due to Dahlberg for computing the numbers of consanguineous matings to be expected under random mating fail in the case of overlapping generations. The concept of random mating can be extended to cover overlapping generations by making the chance of mating between a male and female depend on the interval between their dates of birth. This concept of random mating is illustrated by a numerical example based on a simple hypothetical organism. The implications of the suggested concept of random mating can be explored for species with complicated demographic characteristics, and man in particular, by means of a mathematical model in continuous time. Calculations of the frequencies of various types of consanguineous marriage to be expected under random mating are presented and compared with statistics of consanguineous marriages occurring in various countries. Discrepancies and similarities between observed and theoretical values are discussed.