The objective of this study was to infer (co)variance components for piglet survival at birth in purebred and crossbred pigs. Data were from 13,643 (1,213 litters) crossbred and 30,919 (3,162 litters) purebred pigs, produced by mating the same 168 purebred boars to 460 Large White-derived crossbred females and 1,413 purebred sows, respectively. The outcome variable was piglet survival at birth as a binary trait. A Bayesian bivariate threshold model was implemented via Gibbs sampling. Flat priors were assigned to the effects of sex, parity of the dam, litter size, and year month of birth. Gaussian priors were assigned to litter, dam, and sire effects. Marginal posterior means of the sire and dam variances for liability of piglet survival in purebred were 0.018 and 0.077, respectively. For crossbred, sire and dam variance estimates were 0.030 and 0.120, respectively. The posterior means of the heritability of liability of survival in purebred and crossbred and of the genetic correlation between these traits were 0.049, 0.091, and 0.248, respectively. The greatest 95% confidence region (−0.406, 0.821) for the genetic correlation between purebred and crossbred liabilities of piglet survival included zero. Results suggest that the expected genetic progress for piglet survival in crossbreds when selection is based on purebred information may be nil.