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To study time-dependent characteristics of a population, we may sample the same population at regular intervals. A basic problem is how the sample should be selected at different time periods. Here we consider successive sampling with partial replacement of units on two occasions from a Bayesian point of view. Bayes estimators and optimal designs for such priors will be obtained. In one situation, the whole survey, i.e. the first sample and the second sample, is planned before the first time period t. In another situation, we can use the information from the first sample for the planning of the second sample. So we consider a stagewise procedure. The prior distribution is updated after the first sample is observed at time t. Bayes estimators are derived and the optimal designs for either the ‘second’ sample only, after the first time period t, or ‘both’ samples, before the first time period t, are obtained.