Three farms 3,764 behavioral test (PC) records were used during the period 1981-2019 that corresponded to Charolais (Cha) and Chacuba (Chac) animals. Edited data were studied according to the univariate animal model (M1) for each genotype. In a second step, they were studied jointly, including in all cases the fixed regression coefficients due to the additive genetic components, heterosis and gene recombination of the animals in alternative models according to the univariate additive model (M2), the multivariate additive model (M3) that assumes that the weight in purebred and crossbred animals correspond to different but correlated traits and finally, a nonlinear model (M4). The results obtained were: h2 =0.28±0.10 and h2 =0.32±0.13 for weight at 18 months in purebreds and crossbreds, respectively in M1. For M2 h2=0.22±0.05 and h2=0.28±0.06 and h2=0.32±0.13 in purebreds and crosses in M3 while h2=0.28±0.05 in M4. In M3, the genetic correlation (rg) between the same trait in both types of animals was 0.77±0.30. The results of h2 of the M4 were an intermediate point with respect to the M3 while the precision of the estimated breeding values ??(VG) was slightly higher. Genetic relationships between the VG purebred and crossbred animals in the different models were greater than 0.98 in all cases. The results show that the same trait evaluated in purebred does not correspond to the same character in its cross progenies, although they were correlated. Joint evaluation using multivariate models is the most recommended option for the breeding program since it can provide superior results with the same available data regarding the possible response of an individual analysis of each type of crossbreeds.
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