A total of 94469 test day records of milk yield and milk composition (fat, protein and dry matter contents) from 9271 Payoya goats, collected between November 2002 to December 2007 were analyzed using random regression models to estimate the parameter genetic for these traits. A third order equation for genetic and environment permanent effects, with a heterogeneous residual variance model was the best fit model. For all the traits analyzed results show an increase trend in the heritability values through lactation curve, except for milk yield. This shows the highest values in the middle of lactation. Heritabilities ranged from 0.14 to 0.23 for milk yield, from 0.33 to 0.40% for protein content; 0.10 to 0.20 for fat %, 0.26 to 0.40 for lactose % and finally from 0.12 to 0.29 for dry matter. Genetic correlations were positive and high between adjacent records in all traits. There was a wide genetic variability in the shape of the lactation curve.