Mixed model equations to predict additive and nonadditive genetic values also predict specific combining abilities or combination effects among sire and dams or among sires and maternal grandsires (mgs). Current mating programs, utilizing nonadditive genetic variance only by avoiding mating between close relatives to prevent inbreeding depression, could be improved upon by use of predicted combination effects due to nonadditive variation beyond inbreeding. Simulation was employed to evaluate increase in progeny performance from nonrandom mating based on predicted combination effects among sires and mgs over random mating. Nonrandom mating strategies included mate allocation by linear programming, which is optimum, and two approximations, sequential selection based on progeny merit, and sequential selection based on deviation of progeny merit from mgs average. Genetic parameters were heritability equal to .05, .15, or .25 and ratio of dominance variance to phenotypic variance equal to .05, .10, or .15. These dominance ratios represent the range of recent estimates for yield and type traits. A total of 400 bulls were grouped by .99, .85, and .70 PTA reliability, with the first group being sires and mgs of the others. Using recurrence equations for combination effects, a matrix of true combination effects among the bulls was created. Reliabilites for estimated combination effects were computed for three types of bull populations; one with much information available (.41 to .79 ), one with little information ( .15 to .41 ) and one with an intermediate amount of information available (.15 to .79) and used to form matrices of estimated combination effects. Herds consisted of cows sired by .99 and .85 reliability bulls. Four mating groups of 123 cows, mated to 10 bulls from all bull groups, produced heifers to replace the herd. Herds were replicated 20 times for each type of bull population and each combination of heritability and dominance ratio. The three nonrandom mating strategies yielded means significantly different from random mating (p ≤ .05). When scaled by the standard deviation of milk yield, gains made by linear programming were 12.3 to 40.1 kg for low-reliability populations, 16.4 to 46.4 kg for intermediate reliability populations, and 31.0 to 80.3 kg for high reliability populations. Herds modified to utilize embryo transfer had less gain in progeny merit due to combination effects (20kg) with nonrandom mating compared to non-ET herds with identical heritability and dominance ratio, when donor cows were selected by estimated breeding value. Selection of donor cows based on combination effects yielded large gains (90.72kg) but such selection would only be justified in populations where nonadditive variance was more important than additive. A procedure for routinely approximating reliabilites of combination effects using information from three sources (information on parent subclasses, information on progeny subclasses, and records in subclass of interest) was presented. / Master of Science