Peer-to-Peer networks are gaining increasing attention from both the scientific and the large Internet user community. Popular applications utilizing this new technology offer many attractive features to a growing number of users. At the heart of such networks lies the data retrieval algorithm. Proposed methods either depend on the network-disastrous flooding and its variations or utilize various indices too expensive to maintain. In this report we describe an adaptive, bandwidth-efficient and easy to deploy search algorithm for unstructured Peer-to-Peer networks, the Adaptive Probabilistic Search method (APS). Our scheme utilizes feedback from previous searches to probabilistically guide future ones. Extensive simulation results show that APS achieves high success rates, increased number of discovered objects, very low bandwidth consumption and adaptation to changing topologies. UMIACS-TR-2003-21