In many scientific studies requiring simultaneous testing of multiple null hypotheses, it is often necessary to carry out the multiple testing in two stages to decide which of the hypotheses can be rejected or accepted at the first stage and which should be followed up for further testing having combined their p-values from both stages. Unfortunately, no multiple testing procedure is available yet to perform this task meeting pre-specified boundaries on the first-stage p-values in terms of the false discovery rate (FDR) and maintaining a control over the overall FDR at a desired level. We will present in this talk two procedures, which extend the classical Benjamini-Hochberg (BH) procedure and its adaptive version, and are theoretically proved to control the overall FDR under certain dependence. We consider two types of combination function, Fisher's and Simes', to carry out the proposed procedures. Our simulations indicate that the proposed procedures can have significant power improvements over the BH procedure based on the first stage data relative to the improvement offered by the ideal BH procedure. The proposed procedures will be illustrated through a real gene expression data. This is joint work with Sanat Sarkar and Jingjing Chen.