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Rules are presented for assigning coefficients to the genetic group portion(s) of the mixed model equations after transformation to solve directly for total genetic value (group plus animal solutions) simultaneously for sires and cows using an animal model. Inclusion of all known relationships seems to reduce the need for groups to account for genetic selection and genetic trend. Migration of animals into a population, however, results in a need for grouping to account for genetic merit of the migrants. Selection of parents on which records are not available also creates a need for grouping. Group solutions represent the average genetic merit of phantom (unidentified, or represented by only one descendant) animals selected to be parents that do not have records available. Groups can be crossclassified with time and the genetic path of selection. The total genetic value for every animal includes a function of genetic groups. The function of genetic groups is specific for each individual animal and depends on the number of generations to the base phantom ancestors and on the genetic groups to which those phantom ancestors are assigned. The group coefficients presented account for genetic selection that cannot be defined by known genetic relationships.