The purpose of this paper is to derive estimation procedures; namely Maximum Likelihood (ML), Residual Maximum Likelihood (RML) and Minimum Norm Quadratic Unbiased estimates (MINQUE), for estimating the parameters and variance components in linear models with repeated measurements data. In these models individual's regression coefficients are subject to both fixed and random effects over different individuals. An iterative procedure is proposed for solving the ML and RML equations and the MINQUE estimates are also obtained. A closed form solutions for these methods are derived for growth curve models when the design matrices are the same for each individual.