Breeding value prediction for dairy goats in Germany is still based on herd mate comparison within breeding society. The objective of this study was to estimate genetic parameters for milk yield based on a test day model. For the analysis 35 308, 30 551 and 23 640 test day records from lactations 1, 2 and 3 from 5079, 4118 and 3132 animals, respectively, were used. The data between 1987 and 2003 were obtained from six German breeding societies. The multiple trait (lactations 1, 2 and 3) repeatability model (RPT) included the fixed effects of breeding society–breed–herd–year, litter size, lambing season, and days in milk of third-order Legendre polynomials nested within herd–year, and the random effects of animal additive and permanent environment. The three-trait random regression model (RR) also included the random regressions based on second-order Legendre polynomials for animal additive and permanent environmental effects. Heritability estimates in RPT were 0.27 ± 0.02, 0.20 ± 0.02 and 0.37 ± 0.02 for the first, second and third lactation, respectively. The genetic correlation between the first and second lactation was 0.69, between the second and third lactation 0.79, and between the first and third lactation 0.45. Heritability estimates from the RR in the first and second lactations decreased from the beginning to the end of the lactation, with average values of 0.28 and 0.27, respectively. Estimates in the third lactation showed a maximum in the middle of lactation, averaging 0.37. Genetic correlations between the first and second lactation averaged 0.64, between the second and third lactation 0.72, and between the first and third lactation 0.46. Despite the small data set and restricted relationship structure the estimates were reasonable with the exception of estimates from the third lactation, which seemed inflated. RR could be used for genetic evaluation of dairy goats in Germany.