Brazil has increasingly used advanced techniques of sustainable management, with which the planted forest sector has grown. Advances achieved in the Brazilian forestry sector are significant, especially when we speak of productivity. Therefore the aim of this work to estimate the quantitative genetic parameters of the progenies under the effect of frost and to select the best progenies to subsidize the improving program of Eucalyptus dunnii. The experiment was installed in the city of Palma Sola - SC (Palmasola Company) in 2016, being the weather of the planting site of Cfa type, subtropical, with frost occurrence. The statistical design was carried out through randomized blocks with 163 Eucalyptus dunnii progenies, being two clonal witnesses, six replicates and six plants per plot. The spacing used for the planting of the tests was 3 x 2 meters with double external border. The evaluated characteristics were: Total height of the plants, tortuosity of the stem and the percentage of bifurcated plants, fallen and broken. The evaluation of frost resistance was done indirectly through a scale of grades varying from 1 to 5. The components of variances and genetic parameters were estimated using the REML / BLUP procedure. The percentage of plant survival was 93%. It was observed that some plants suffered intense damage, of damage equal to 4. The percentage of bifurcated plants at 07 months of age was 3,81% similar to that found in the sum of fallen and broken trees. As for the percentage of stable progenies (without bifurcations, falls or breaks) was 86,41%. More than 50% of the progenies were tolerant once they did not suffer any visual damage, regarding the two age range in which they were evaluated. The ground varied during the time of the two evaluations, presenting values from 0,28 to 0,86. The h²mp% in the two evaluations were of high magnitude (0,58 to 0,82). The accuracy for height, stem shape and frost were above 76% at all ages, indicating good accuracy of selection and higher genetic gain. Regarding CVexp% for height and stem shape, they got mean values, which suggests one has got a good experimental accuracy in the attaining of parameters. Genetic and phenotypic correlations between the variables were mostly weak (<0,50) and negative for the ages evaluated, indicating that the indirect selection will not be a good alternative and that in general, the variables evaluated are independent. We observed that 54,86% of the progenies got grade 1. There is presence of genetic variability, this genetic variation. Heritabilities (h²) were medium to high for damage caused by frost, simple methods may be efficient in selection. All variables, in general, presented low genetic and phenotypic correlations among themselves, showing that the indirect selection is not efficient for the characters evaluated in this population; We selected 32 progenies that presented potential for frost tolerance.
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