Abstract This study had two aims. Firstly, we wanted to quantify the effects of breed and parity on lactation curves. A parametric model for describing milk yield for cows [Friggens, N., Emmans, G., Veerkamp, R., 1999. On the use of simple ratios between lactation curve coefficients to describe parity effects on milk production. Livest. Prod. Sci. 62, 1–13] was used. The data contained 155,051 daily records of milk yield from 318 cows of three different breeds; Danish Red, Danish Holstein and Jersey. There were 276, 230, and 98 lactation curves for parities 1, 2 and 3 respectively. For every cow lactation, the parameters of the model were estimated using a least squares procedure for non-linear models. The resulting parameters were analysed in a mixed linear model. Significant effects of parity were observed on the same two parameters as in Friggens et al. [Friggens, N., Emmans, G., Veerkamp, R., 1999. On the use of simple ratios between lactation curve coefficients to describe parity effects on milk production. Livest. Prod. Sci. 62, 1–13]. Breed was also found to have a significant effect on some of the parameters. However, there was no significant interaction between breed and parity. The second aim of the study was to evaluate the properties of acceleration in milk yield in the context of providing an indicator for physiological stress and subsequent health problems. Milk yield acceleration was highest around calving and also reflected trends for higher stress/risk for higher yielding cows.