It was evaluated in this work the components of (co)variance and heritability of the parameters of egg production curve in quails in a model of double stages: the first stage is composed of the adjustment of a nonlinear curve, and the second is composed of the assessing of the genetic parameters obtained by the animal model. It was used daily individual records from laying to 90 days, starting with the first egg in the batch, of 308, 374 and 378 birds from three lines. In each strain, there was no difference between the components of (co)variance neither heritability for rations containing different energy levels (2,900 or 2,500 kcal/kg ME), indicating that there was no heterogeneity of variance. However, values of genetic correlations were in the order from 0.53 to 0.65 for the α parameter and, for β from 0.28 to 0.30, indicating one existing genotype x environment interaction. Estimates of heritability, respectively in the three lines, for the α and β parameters in the high energy diet were 0.21 and 0.50, 0.12 and 0.49, 0.12 and 0.48, and for the low energy diet 0.23 and 0.50, 0.13 and 0.50, 0.10 and 0.47. Estimates of the components of (co)variance and heritability were different among the lines, for the two curve parameters. One line showed higher heritability for the α parameter, indicating greater potential for changes by selection for production at the initial stage of laying. Considering the β parameter, the three lines have the same potential.
