Procedures for calculating the additive genetic variance-covariance matrix and its inverse are adapted to accommodate the occurrence of mutations in the genome. The inverse matrix can be used in mixed model methodology for best linear unbiased prediction of breeding values or for variance component estimation under a genetic model that includes mutation effects. In the mixed model methodology (Henderson, 1973) used in animal breeding to predict breeding values of animals, the additive genetic variance-covariance matrix (or, in fact, its inverse) is included with the aim of increasing the accuracy of prediction by accounting for all the additive genetic variances and covariances between individuals. In this way, the reduction in additive genetic variance (0:) due to inbreeding and to selection is intrinsically accounted for (Sorenson and Kennedy, 1984). However, these decreases in additive genetic variance may be counterbalanced to some extent by the occurrence of mutations of the genome. Genomic mutations include base pair substitution, duplications, insertions, and inversions of segments of chromosomes. They may occur at neutral sites (e.g., at introns or inactive sites), at active sites but at loci that are neutral with respect to the quantitative trait of interest, or at loci that affect the trait. In the latter case the new mutations would serve to increase a:. Mutation has been offered as one explanation for the continued response in long-term selection experiments in which the attainment of a selection plateau might be expected, for example, more than 50 generations of selection for oil in maize (Dudley, 1977). Hill (1982) examined the effects of mutation on response to selection by simulation and concluded that although mutation events had little impact on the initial generations of selection programmes, they should not be ignored in the design and analysis of long-term experiments, nor in the analysis of data on many generations from small animal populations, e.g., pigs and poultry. Inclusion of the effects of mutation into an additive genetic mixed model therefore seems important for the analysis of some animal breeding data (Dempfle, 1987; Dempfle and Grundl, 1988) and requires that account be taken of variances and covariances between animals accrued by mutations in previous generations, yet not traceable to the base population. Currrent address: The Edinburgh School of Agriculture, West Mains Road, Edinburgh EH9 3JG, Scotland.