genetics parameters and selection gains, obtained 36 months after planting, are presented and discussed for progenies of open pollinated population of a？ai palm for plant height (ap), plant diameter (dpc), number of live leaves ( nfv) and tiller number (np), based on the linear mixed model methodology (reml / blup). the thirty progenies were evaluated in a randomized blocks design with three replications and plots of five plants, spaced at 6m x 4m. the values obtained for individual heritability (0.55, 0.44, 0.38 and 0.43) and for progeny means (0.64, 0.54, 0.58 and 0.64) for ap, dpc, nfv and np, respectively, were expressives, which indicates the possibility of genetic progress with the selection. the accuracy among the genetics values predicted and the true were of 0.802 for height, 0.736 for diameter, 0.760 for number of live leaves and 0.797 for tiller number. with the exception of nfv character, the coefficients of individual genetic variation were high (>10%), confirming the potential of the population for selection. predicted genetic gains of 89.3% were obtained for the character ap and 2.1% for dcp, with the selection of the twenty top individuals. correlation was found between height and diameter of the plant. among ages, for the same characters, positive correlations of mean magnitudes were found.