Resilience is the capacity of an animal to be minimally affected by disturbances or to rapidly return to the state pertained before exposure to a disturbance. Commercial laying hens can be exposed to a large variety of disturbances (e.g. pathogens). There is growing interest to measure and select for improved resilience in farm animals. We aimed at studying the genetic background of resilience indicator traits, their genetic relationship with health- and production-related traits in purebreds and crossbreds. The populations consisted of two egg-laying commercial lines (W and B), with records on purebreds and crossbreds. The purebreds (33,825 W and 34,397 B birds) were individually housed, while the crossbreds were housed in cages of 6 to 8 paternal half-sibs (12,852 W and 3,898 B cages). Recorded traits were egg production (EP), date of death (SURV), and, in purebreds only, natural antibodies titers (NAb). Deviations between weekly EP and their flock’s average were calculated. The resilience indicator traits were the natural logarithm of the variance (LNVAR) and the lag-one autocorrelation (AUTO-R) of these deviations. Genetic parameters of LNVAR and AUTO-R, and their genetic relationships with EP, SURV, and NAb were estimated. In both purebreds, EP was lowly heritable (mean h², = 0.12), SURV was almost not heritable (mean h² = 0.008, P-value ≤ 0.05), NAb were lowly to moderately heritable (mean h² = 0.25), and resilience indicators were lowly heritable (LNVAR: mean h² = 0.11, AUTO-R: mean h² = 0.05). Compared to purebreds, crossbred traits were less heritable for EP (mean h²= 0.05) and AUTO-R (mean h² = 0.02), SURV remained lowly heritable (W:  = 0.02, B:  = 0.00, P-value = 0.12), and LNVAR was slightly more heritable than in purebreds (mean h² = 0.16). The genetic correlations between purebreds and crossbreds were lower than 0.80 in both lines (rpc from -0.55 to 0.63), meaning crossbreds’ traits were different from purebreds’ traits. In both purebreds and crossbreds, LNVAR and AUTO-R traits displayed favorable genetic correlations among themselves, and with EP, SURV, and NAb. These results suggest that selection for resilience based on big data can be implemented in breeding programs to improve health and production of laying hens. Cross-validation is now required to investigate if selection for improved resilience in purebreds results in improved resilience in crossbreds.