In the analysis of longitudinal data, before assuming a parametric model, an idea of the shape of the variance and correlation functions for both the genetic and environmental parts should be known. When a small number of observations is available for each subject at a fixed set of times, it is possible to estimate unstructured covariance matrices, but not when the number of observations over time is large and when individuals are not measured at all times. The non-parametric approach, based on the variogram, presented by Diggle & Verbyla (1998), is specially adapted for exploratory analysis of such data. This paper presents a generalization of their approach to genetic analyses. The methodology is applied to daily records for milk production in dairy cattle and data on age-specific fertility in Drosophila.