The basic objectives and procedures for successful crossbreeding of beef cattle were considered, with special reference to the levels of realized hybrid vigor that might be anticipated for different crossbreeding programs involving the American Brahman (Z1) and European (Ej) breeds. Intralocus heterozygosis levels with respect to breed origin of genes (breed heterozygosis) were computed for various crossbreeding systems. These values were weighted by approximate relative F1 heterosis levels for different breed combinations (1.0 for Z1Ej and .3 for E1E2) to yield the estimated relative hybrid vigor levels for total performance in alternative crossbreeding systems. The estimated average maternal heterosis levels for the various systems, were respectively 0, 33, 67, 66, 50, 54 and 49% for production of F1 (EZ) calves, three-breed terminal cross calves, two-breed-of-sire (E1--Z1) rotation crosses, three-breed-of-sire (Z1--E1--E2) rotation crosses, two-breed (Z X E) synthetics, three-breed (Z1 X E1E2) synthetics and four-breed (Z1E1 X E2E3) synthetics. The respective values for calf heterosis levels were 50, 57, 67, 66, 50, 54 and 49%. Successful crossbreeding requires (1) the choice of appropriate breed combinations for the environment and production system management programs to support the increased production potential or crossbred cattle.