ABSTRACT An inbreeding matrix is defined for populations with overlapping generations. In the short term it can be expressed in terms of a matrix specifying the passage of genes between the different age groups (and sexes) and a diagonal matrix whose elements depend on the number of individuals in each age group. Formulae for the inbreeding effective number are derived using matrix theory. A comparison is made between the inbreeding coefficients predicted by this theory and those obtained by assuming a uniform rate of inbreeding from the outset, and these in turn are compared with the exact inbreeding coefficients.