Traditional drug development consists of a sequence of independent trials organized in different phases. Full development typically involves (i) a learning phase II trial and (ii) one or two confirmatory phase III trial(s). For example, in the phase II trials several doses of the new compound might be compared to a control and/or placebo with the goal of deciding whether to stop or continue development and, in the latter case, selecting one or two "best" doses to carry forward into the confirmatory phase. The phase III trials are then conducted as stand-alone confirmatory studies, not incorporating in their statistical analyses data collected in the previous phases. Seamless phase II/III designs are aimed at interweaving the two phases of full development by combining them into one single, uninterrupted study conducted in two stages. In the dose-finding example above, one (or more) dose(s) are selected after the first stage based on the available data at interim, and are then observed further in the second stage. The final analysis of the selected dose(s) includes patients from both stages and is performed such that the overall type I error rate is controlled at a prespecified level regardless of the dose selection rule used at interim. The adequacy of the dose selection at interim is obviously a critical step for the success of a seamless phase II/III trial. In this paper we focus on the description of flexible test procedures allowing for adaptively selecting hypotheses at interim and thus allowing the combination of learning and confirming in a single seamless trial. We review the statistical background, introduce different test procedures and compare them in a power study. In a subsequent paper (Schmidli et al., 2006) we give several applications from our daily practice and discuss related implementation issues in conducting adaptive seamless designs.