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Background: A sufficient IgG content in the colostrum is essential for the newborn calf, as it provides passive immunity which substantially affects the probability of survival during rearing. Failure of passive transfer (FPT) occurs when a calf does not absorb enough antibodies from the colostrum and is defined by an IgG concentration in calf serum lower than 10 g/L. Apart from delayed access to colostrum, FPT can be due to a low production of IgG in the mother or poor IgG absorption by the calf. The aim of this study was to estimate the genetic background of antibody levels and indicator traits for antibodies in the colostrum and calf serum, and their correlation with milk production., Results: Colostrum data were available for 1340 dairy cows with at least one calving and calf serum data were available for 886 calves from these cows. Indicator traits for antibody concentrations were estimated using refractometry (a digital Brix refractometer for colostrum and an optical refractometer for serum), and enzyme-linked immunosorbent assays (ELISA) were used to determine the levels of total IgG and natural antibodies (NAb) of various antibody isotypes in the colostrum and calf serum. Colostrum traits had heritabilities ranging from 0.16 to 0.31 with repeatabilities ranging from 0.21 to 0.55. Brix percentages had positive genetic correlations with all colostrum antibody traits including total IgG (0.68). Calf serum antibody concentrations had heritabilities ranging from 0.25 to 0.59, with a significant maternal effect accounting for 17 to 27% of the variance. When later in life calves produced their first lactation, the lactation average somatic cell score was found to be negatively correlated with NAb levels in calf serum., Conclusions: Our results suggest that antibody levels in the colostrum and calf serum can be increased by means of selection., (© 2022. The Author(s).)