In New Zealand, a large proportion of cows are currently crossbreds, mostly Holstein-Friesians (HF) x Jersey (JE). The genetic evaluation system for milk yields is considering the same additive genetic effects for all breeds. The objective was to model different additive effects according to parental breeds to obtain first estimates of correlations among breed-specific effects and to study the usefulness of this type of random regression test-day model. Estimates of (co)variance components for purebred HF and JE cattle in purebred herds were computed by using a single-breed model. This analysis showed differences between the 2 breeds, with a greater variability in the HF breed. (Co)variance components for purebred HF and JE and crossbred HF x JE cattle were then estimated by using a complete multibreed model in which computations of complete across-breed (co)variances were simplified by correlating only eigenvectors for HF and JE random regressions of the same order as obtained from the single-breed analysis. Parameter estimates differed more strongly than expected between the single-breed and multibreed analyses, especially for JE. This could be due to differences between animals and management in purebred and non-purebred herds. In addition, the model used only partially accounted for heterosis. The multibreed analysis showed additive genetic differences between the HF and JE breeds, expressed as genetic correlations of additive effects in both breeds, especially in linear and quadratic Legendre polynomials (respectively, 0.807 and 0.604). The differences were small for overall milk production (0.926). Results showed that permanent environmental lactation curves were highly correlated across breeds; however, intraherd lactation curves were also affected by the breed-environment interaction. This result may indicate the existence of breed-specific competition effects that vary through the different lactation stages. In conclusion, a multibreed model similar to the one presented could optimally use the environmental and genetic parameters and provide breed-dependent additive breeding values. This model could also be a useful tool to evaluate crossbred dairy cattle populations like those in New Zealand. However, a routine evaluation would still require the development of an improved methodology. It would also be computationally very challenging because of the simultaneous presence of a large number of breeds.