Liveweight data from walk-over-weigh technology on NZ dairy farms provides a potential source of daily or average liveweight data for genetic selection. In this study, fixed and random regression models utilising varying orders of Legendre polynomials or eigenvectors were assessed to model the longitudinal properties of liveweight records of New Zealand dairy cows. Higher orders models fitted the data best despite the subsequently large increase in number of parameters. The choice of either Legendre polynomials or eigenvectors as the basis functions made no significant difference. Limits to model order will need to be applied on the basis of assumptions concerning data covariance structure and desired number of liveweight-derived traits for selection. Additionally, methods developed here for est Zealand imation of genetic covariance of regression coefficients and for efficient inversion of the mixed model equation matrix can be extended to models for which pedigree relationships are also taken into account.