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The present study aimed at evaluating genetically the best progenies of Myracrodruon urundeuva, Astronium fraxinifolium e Terminalia argentea from Selvíria, MS, concerning their growing traits. The progeny test was performed by outlining randomized blocks with 28 treatments, 4 repetitions and 10 plants per plot in single rows at 1.5 x 3.0 spacing. At 14 years of age, the progenies were evaluated concerning the traits: height (ALT, m); diameter of the height (DAP, cm); average diameter of the top (DMC, cm); trunk shape (FT), grade scale, ranging from 1 to 5, and survival (SOB, %). The average herdability for the traits studied is considered from medium to highs magnitudes (0.67; 0.57 e 0.83) for DAP, DMC e trunk shape, respectively. More expressive outcomes were obtained from the average of progenies (9.42; 9.40 e 12.83) for DAP, respectively, which indicates that the selection can be effective using such information, not only from the families but also from the individuals for native progenies from the region which indicates a good perspective of genetic variability to be exploited along a genetic breeding program for the studied species and the establishment of strategies for future formation of a seed orchard.