Many finite populations which are sampled repeatedly change slowly over time. Then estimation of finite population characteristics for the current occasion,l, may be improved by the use of data from previous surveys. In this article we investigate the use of empirical Bayes procedures based on two superpopulation models. Each model has the same first stage: The values of the population units on theith occasion are a random sample from the normal distribution with meanμiand varianceσ2i. At the second stage we assume that either (a)μ1, …,μlare a random sample from the normal distribution with meanθand varianceδ2, or (b) givenσ2iandτ,μihas the normal distribution with meanθand varianceσ2iτ(independently for eachi), whereas theσ2iare a random sample from the inverse gamma distribution with parametersη/2 andκ/2. In (a) theσ2i,θ, andσ2are assumed to be unknown, whereas in (b)θ, τ, andκare unknown. We develop empirical Bayes point estimators and confidence intervals for the finite population mean on thelth occasion and make large-sample comparisons with the corresponding Bayes estimators and intervals. These are asymptotic results obtained within the framework of “classical” empirical Bayes theory. To complement the asymptotic results we present the results of an extensive numerical investigation of the properties of these estimators and intervals when sample sizes are moderate. The methodology described here is also appropriate for “small area” estimation.