Up to 109,447 records of 49,656 Large White sows were used to evaluate the genetic relationship between number of pigs born dead (BD) and number born alive (BA) in first and later parities. Performance data (n = 30,832) for ultrasound backfat (BF) at the end of the test and days to reach 113.5 kg (AD) were used to estimate their relationships with BD and BA at first parity in a four-trait threshold-linear analysis (TL). Effects were year-farm, contemporary group (CG: farm-farrowing year-farrowing month) and animal additive genetic. At first parity, estimates of heritability were 0.09, 0.09, 0.37, and 0.31 for BA, BD, AD, and BF, respectively. The estimate of genetic correlation between BD and litter size was -0.04 (BD-BA). Corresponding values with test traits were both -0.14 (BD-AD, BD-BF). Estimates of genetic correlation between BA and performance traits were 0.08 (BA-AD) and 0.05 (BA-BF). The two test traits were moderately negatively correlated (-0.22). For later parities, a six-trait (BD, BA in three parities) TL model was implemented. The estimates of additive genetic variances and heritability increased with parity for BD and BA. Estimates of heritabilities were: 0.09, 0.10, and 0.11 for BD, and 0.09, 0.12, and 0.12 for BA in parities one to three, respectively. Estimates of genetic correlations between different parities were high (0.91 to 0.96) for BD, and slightly lower (0.74 to 0.95) for BA. Genetic correlations between BD and BA were low and positive (0.02 to 0.17) for BA in Parities 1 and 2, but negative (-0.04 to -0.10) for BA in Parity 3. Selection for increased litter size should have little effect on farrowing piglet mortality. Intense selection for faster growth and increased leanness should increase farrowing piglet mortality of first-parity sows. A repeatability model with a simple correction for the heterogeneity of variances over parities could be implemented to select against farrowing mortality. The genetic components of perinatal piglet mortality are independent of the ones for litter size in the first parity, and they show an undesirable, but not strong, genetic association in second parity.