Genetic parameters for milk yield of first lactation Spanish Hosltein cattle were estimated using test day models. Different alternative models were employed and were compared in terms of goodness of fit and predictive ability using cross validation techniques. Models used were repeatilbility model (MMR) and different random regression models (MRA), using Wilmink function, Ali‑Schaeffer function and Legendre polynomials. The MRA were better than MMR. Within the MRA, those models which fitted Legendre polynomials were better than those which fitted lactational funtions. Moreover, the MRA had the disadvantage that they did not describe well the genetic parameters at the onset and at the end of lactation when the order of fit for additive effect was greater than four. This problem was not observed when the high orders of fit for permanent effect were used. Furthemore, when the order of fit for permanent effect increased, the improving of the model was better than when the increasing of order was carried out for the additive effect.