To study the genetic determinism of propagation by cutting, 2,115 individuals of 83 full-sib families of the Eucalyptus urophylla×Eucalyptus grandis hybrid were used as stock plants and propagated by cuttings. Shoot production (PROD) and cutting success (CUT) were measured in two periods corresponding to the dry and rainy seasons. The experiments showed a significant effect of propagation period, suggesting the combined influence of environmental conditions and physiological state of stock plants. Using the linear mixed model (LMM) and the generalized one (GLMM) to take into account the non-normal distribution, the additive and dominance variances were estimated. They were significantly different from zero for PROD and CUT, as was the interaction between genetic effects and periods. The dominance variance was equal or higher than additive variance for both traits (1 <?2 D/?2 A<1.5). Broad- and narrow-sense heritabilities change with the model type. For PROD, with LMM, they were moderate (h2 ss=0.182 and H2 sl=0.443) but high with GLMM (h2 ss=0.431 and H2 sl=0.891). For CUT, the same trend was observed for variances but the genetic control was weaker with heritabilities smaller than 0.3. The selection accuracy (r) was affected by the statistical model, r=0.94 and r=0.42 for PROD using LMM and GLMM, respectively. Genetic correlations between PROD, CUT, and the field growth of clones at 25 months were relatively low. These results are important elements to consider for breeding strategies that target genetic gain for both field growth and cutting success.