¹Department Animal Science, Faculty of Agriculture, University of Ondokuz Mayis, TR-55139 Samsun - TURKEY DOI : 10.9775/kvfd.2020.22903 In this study, it was aimed to estimate covariance function, covariance components, permanent environmental effect, additive genetic effect and heritability values, and comparison of models with different order and heterogeneous residual variances Legendre Polynomials in the first lactation Turkish Holstein cows more than 10 test day milk yields. For this aim, 7340 test day records of 386 Holstein Friesian cows in the first lactation raised in private dairy farm calving from 2013 to 2018 in Kırşehir-Turkey were used. The six Legendre polynomial models by random regression described as L(2,2), L(3,3), L(4,4), L(5,5), L(6,6) and L(7,7) were evaluated using first lactation test day records. Heterogeneous residual variances (RV) were modeled by considering five sub-classes. Analyzes were performed using the WOMBAT statistical package. In comparison of the models, -2LogL, Akaike Information Criterion (AIC), Bayes Information Criterion (BIC) and RV were used. Also, the compatibility of random regression models was examined in terms of eigenvalues of covariance matrices. The values of -2LogL (between 28334.16 and 26610.07), AIC (between 28356.16 and 26732.07) and BIC values (between 28432.05 and 27129.21) obtained from the study result decreased as the model order increased. As a result, it was determined that the 3rd degree Legendre polynomial model can provide sufficient compliance. However, when looking at the values for -2LogL, AIC and RV, it was determined that the L(7,7) model fits well according to other models. Keywords : Heritability, Permanent environmental effect, Additive genetic effect, Holstein Friesian, First lactation