We describe the adaptive source routing (ASR) method which is a first attempt to combine adaptive routing and source routing methods. In ASR, the adaptivity of each packet is determined at the source processor. Every packet can be routed in a fully adaptive or partially adaptive or non-adaptive manner, all within the same network at the same time. We evaluate and compare performance of the proposed adaptive source routing networks and oblivious routing networks by simulations. We also describe a route generation algorithm that determines maximally adaptive routes in multistage networks.