To identify superior genotypes, 42 progenies of interspecific hybrids between American oil palm and oil palm were evaluated in an area with incidence of bud rot. The following variables were assessed: total bunch yield (TBY), number of bunches (NB) and mean bunch weight (MBW) from the third to the sixth year of cultivation and estimates of genetic parameters obtained by REML/BLUP procedures. High heritability values of the evaluated traits were observed. The gain estimates for TBY were 14.49% for the selection of the five best progenies and 33.36% for the selection of the five best trees, considering multiplication by cloning. A medium correlation was observed between TBY and NB (r2 = 0.33±0.021), a high correlation between TBY and MBW (r2 = 0.53±0.019) and a negative high correlation between NB and MBW (r2 = –0.60±0.018). The results indicate a high expectation of gains with selection for TBY