We consider a pharmaceutical Research & Development (R & D) pipeline management problem under two significant uncertainties: the outcomes of clinical trials and their durations. We present an Approximate Dynamic Programming (ADP) approach to solve the problem efficiently. Given an initial list of potential drug candidates, ADP derives a policy that suggests the trials to be performed at each decision point and state. For the classical R&D pipeline planning problem with deterministic trial durations, we compare our ADP approach with other methods from the literature, and find that it can find better solutions more quickly in particular for larger problem instances. For the case with stochastic trial durations, we compare the ADP algorithm with a myopic approach and show that the expected net profit obtained by the derived ADP policy is higher (almost 20% for a 10-drug portfolio).