Genetic parameters of kit survival traits and birth weight were estimated on ITELV2006 synthetic line aimed at improving kit survival using a multiple trait linear and threshold model. Data on 1696 kits for survival at birth and at weaning, as well as individual birth weight and litter size were analysed. Genetic effects of kit survival traits and birth weight were estimated based on threshold and Gaussian models, respectively, using a Bayesian approach. The statistical model included, as fixed effects, parity, lactation status, season of farrowing, nest status, cannibalism in kit, place of kit’s birth in the cage and gender, and adjustment for litter size. Posterior means of heritabilities for direct genetic effects of survival at birth and the entire nursing period, as well as birth weight, were 0.018, 0.023, and 0.088, respectively, and were increased when adjusted for litter size to 0.021, 0.027 and 0.146. Genetic correlation between survival traits was zero. Therefore, these traits can be treated genetically as different traits. Genetic correlation between direct effects of survival at birth and birth weight showed positive, but low, value (+0.134) and was increased to +0.535 when the traits were adjusted for litter size. No genetic correlation was found between survival at weaning and birth weight. These magnitudes of genetic parameter estimates suggested that there is substantial potential for the genetic improvement of kit survival at birth through selection for birth weight.