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• The study focuses on health and routinely collected traits in Holstein cattle. • The events of health problems and culling were investigated in Holstein cattle. • The heritability and genetic correlation of health traits were estimated. • The approximate genetic correlations were estimated between health and routinely collected traits. • The results are beneficial for disease−resistance breeding in Holstein cattle. Health traits have high economic values in dairy cattle breeding, which can cause considerable financial loss through involuntary culling. In this study, fourteen health traits were analysed, including five composite health traits: reproductive disorders, udder health (UH), digestive disorders, metabolic disorders, locomotory diseases (LD), and nine independent health traits: gestation disorders and peripartum disorders, irregular estrus cycle and sterility, metritis (ME), mastitis (MA), abomasal displacement (AD), enteritis (EN), and ketosis, claw diseases (CD), laminitis complex. This study analysed variance components for health traits through both single and bivariate repeatability animal models. All health traits showed low heritability, ranging from 0.001 to 0.025. Most of the health traits in five categories showed negative genetic correlations, ranging from −0.012 (CD and EN) to −0.634 (ME and EN). Strong positive genetic correlations appeared within the same category, ranging from 0.469 (EN and AD) to 0.994 (UH and MA, LD and CD). Furthermore, approximate genetic correlations were evaluated between health traits and routinely collected traits (longevity, fertility, production, and conformation). In general, the low to moderate approximate genetic correlations were estimated between health traits and routinely collected traits. The estimated correlations between health traits and longevity, fertility, production, and conformation traits could provide an indirect reference for disease−resistance breeding in Holstein cattle. [ABSTRACT FROM AUTHOR]