Many longitudinal surveys can be represented as two-phase samples, where the entire set of observed units can be considered to be a first-phase sample and the second-phase samples are panels that are observed at times determined by an observation scheme. Common longitudinal schemes such as pure panel, rotating panels, and supplemented panels fit this two-phase sample description. We propose a cell-mean model with a fixed number of time points and panels where the model links the vector of second-phase panel means to the vector of time point population means. Covariance matrix estimation techniques that rely on fitting theoretical autocovariance functions to empirical covariances using nonlinear least squares are presented. A method for pooling covariance estimators across partially overlapping panels is described. The estimated generalized least squares estimator (EGLSE) is proposed for the vector of time means. Given a consistent first-phase replication variance estimator, the properties of a consistent replication estimator for the variance of the EGLSE are derived. A central limit theorem for the mean vector is given for the EGLSE under stratified fixed-rate second-phase sampling. We examine weight adjustments and imputation procedures for creating an output dataset that reflects the EGLSEs for key variables. Weight adjustment through regression estimation is proposed for a dataset containing a panel that is always observed and the replication variance estimator is extended to the regression estimator. For constructing a complete dataset, we consider imputation methods where the imputed values are chosen so that the weighted total equals the EGLSE. Results are illustrated using the National Resources Inventory, which has a supplemented panel design.