With the development of automatic self-feeders and electronic identification, automated, repeated measurements of individual feed intake (FI) and BW are becoming available in more species. Consequently, genetic models for longitudinal data need to be applied to study FI or related traits. To handle this type of data, several flexible mixed-model approaches exist such as character process (CPr), structured antedependence (SAD), or random regression (RR) models. The objective of this study was to compare how these different approaches estimate both the covariance structure between successive measurements of FI and genetic parameters and their ability to predict future performances in 3 species (rabbits, ducks, and pigs). Results were consistent between species. It was found that the SAD and CPr models fit the data better than the RR models. Estimations of genetic and phenotypic correlation matrices were quite consistent between SAD and CPr models, whereas correlations estimated with the RR model were not. Structured antedependence and CPr models provided, as expected and in accordance with previous studies, a decrease of the correlations with the time interval between measurements. The changes in heritability with time showed the same trend for the SAD and RR models but not for the CPr model. Our results show that, in comparison with the CPr model, the SAD and RR models have the advantage of providing stable predictions of future phenotypes 1 wk forward whatever the number of observations used to estimate the parameters. Therefore, to study repeated measurements of FI, the SAD approach seems to be very appropriate in terms of genetic selection and real-time managements of animals.