The results of simulated selection of bulls are presented; the bulls were tested for the fat content in the milk of daughters. The database contained data on 250 bulls of the Slovak Pied cattle. The progenies of above-average sires (3) and above-average sires of mothers were chosen during the selection process. That means the progenies were half-sisters of the tested bulls, or half-sisters of the mothers of the tested bulls. Selection type 4 - 3 represented an average fat content increase by 0.02 % and 0.01 %, respectively. The increase was somewhat higher (up to 0.04 %) if selection was based on the breeding value. Regression as can be seen in Fig. 1 was observed for all types of selection (with respect to the level higher than the mean of the given group or to the best and worst individuals). In Tabs. I to IV there are values of the average fat contents in the milk of the daughters or all bulls in the whole population and in the daughters of bulls which came from the selected (above-average) individuals. Phenotype values of the progeny (daughters of bulls, daughters of sires, daughters of sires of the mother) were compared for each case. The effects of selection were determined in such cases when the tested bulls were selected on the basis of the performance level of their half-sisters after the sire and on the basis of the performance of the half-sisters of their mother. Significant correlations +0.175++ (for the first lactation) and +0.199++ (for all lactations) were only found between the performance (milk fat content) of the mother and the performance of the daughters of the mother's sire (half-sisters of the bull's mother). These results confirm the results of the paper by Novy and Candrak (1990), where selection for milk and fat production in kg was simulated. The correlation coefficients presented in this paper were +0.216+ (fat yield in kg) and +0.208++ for the FCM yield.