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Longissimus muscle area, shear force measure, and sensory panel scores for flavor, juiciness, and tenderness, and marbling score were obtained from 682 steer carcasses, resulting from crosses among five Bos taurus and Bos indicus breeds. The single-trait model used included birth year and as covariates breed fractions, weaning age, and days on feed. The numerator relationship matrix was for 1,350 animals (682 steers, 74 pure breed and 52 F1-cross sires and 542 dams). The coefficient matrix was inverted to examine standard errors of prediction. Estimated breeding value is the sum of the estimate of genetic deviation and the weighted (fractions) sum of estimates of breed effects. Heritabilities used in estimating breeding values were .62, .06, .05, . 1 1, .05, and .43 for longissimus muscle area, shear force, flavor, juiciness, tenderness, and marbling score. Sires within a breed or crossbred group tended to rank similarly due to large differences among breed effects (e.g., the six Sahiwal sires ranked in the highest six places for shear force). These results illustrate that for traits with large breed differences, selection of the proper breed should be done before selection within that breed.