ABSTRACT Data from 83,088 Hereford and Braford cattle were used to compare parameters and breeding values obtained using linear and threshold models for visual scores of limb conformation (LCW and LCY), breed traits (BTW and BTY), sexual traits (STW and STY), eye pigmentation (EPW and EPY), and navel size (NSW and NSY) at weaning and yearling, respectively. Additionally, principal component analysis was applied to investigate the relationship among the estimated breeding values. Higher direct heritability were estimated using the threshold model (ranging from 0.134±0.021 to 0.194±0.023) compared with the linear model (ranging from 0.085±0.008 to 0.120±0.009). Rank correlations between breeding values predicted using linear and threshold models ranged from 0.61 to 0.88 (LCW), 0.53 to 0.91 (BTW), 0.66 to 0.87 (STW), 0.80 to 0.96 (EPW), 0.87 to 0.95 (NSW), 0.70 to 0.92 (LCY), 0.49 to 0.93 (BTY), 0.56 to 0.95 (STY), 0.88 to 0.97 (EPY), and 0.80 to 0.95 (NSY). The low genetic variability of the studied traits suggests a small genetic gain in the morphology and adaptation. According to the results obtained in the rank correlation, the percentage of coincident animals and the cross-validation analyses, it is recommended to use the threshold model for limb conformation, breed, and sexual traits. For eye pigmentation and navel size scores, both models can be used. In practical terms, the producer will be able to carry out his own selection, considering other traits that are not currently incorporated in the selection indexes, but that can lead to simultaneous gains in the morphology and adaptation of Hereford and Braford cattle. 83088 83 088 83,08 LCW LCY, LCY , LCY) BTW BTY, BTY BTY) STW STY, STY STY) EPW EPY, EPY EPY) NSW NSY yearling respectively Additionally ranging 01340021 0 134 021 0.134±0.02 0.194±0.023 01940023 194 023 00850008 085 008 0.085±0.00 0.120±0.009. 01200009 0.120±0.009 . 120 009 0.120±0.009) 061 61 0.6 88 0.8 LCW, (LCW) 053 53 0.5 091 91 0.9 BTW, (BTW) 066 66 087 87 STW, (STW) 080 80 096 96 EPW, (EPW) 095 95 NSW, (NSW) 070 70 0.7 092 92 (LCY) 049 49 0.4 093 93 (BTY) 056 56 (STY) 097 97 (EPY) NSY. (NSY) correlation crossvalidation cross validation analyses terms indexes 8308 8 08 83,0 0134002 13 02 0.134±0.0 0.194±0.02 0194002 19 0085000 00 0.085±0.0 0120000 0.120±0.00 12 06 6 0. 05 5 09 9 07 7 (LCY 04 4 (BTY (STY (EPY (NSY 830 83, 013400 1 0.134±0. 0.194±0.0 019400 008500 0.085±0. 012000 0.120±0.0 01340 0.134±0 0.194±0. 01940 00850 0.085±0 01200 0.120±0. 0134 0.134± 0.194±0 0194 0085 0.085± 0120 0.120±0 013 0.134 0.194± 019 0.085 012 0.120± 01 0.13 0.194 0.08 0.120 0.1 0.19 0.0 0.12