The problem of docking with a passive orbiting object which is either spinning or tumbling has recently developed interest for several reasons. Retrieval and repair of spent satellites will be technically feasible and economically desirable with the advent of the space shuttle system. Manned space stations will be circling the globe within a few years; thus, indicating that elimination of at least part of the space debris may be imperative to insure safety from collisions. Many of the discarded items are spinning and have a wide variety of shapes and sizes. Furthermore, if a collision or other mishap should occur, a manned vehicle may become uncontrolled and enter a tumbling mode of attitude motion. In order to rescue the crew or repair the spacecraft, this tumbling must be controlled and eliminated. Many studies have been carried out to formulate rescue schemes and requirements, develop uncooperative rendezvous techniques, and investigate satellite manipulation via remote operators. However, several specific problems related to docking with objects possessing angular momentum have not previously been considered and require new technology for solution. Techniques for retrieving uncooperative spinning objects are presented. A conceptual spacecraft for remotely despinning and retrieving debris of moderate size is discussed in depth. In addition, the more complex problems of detumbling a large vehicle are described. Specific aspects of rescue from such a vehicle are presented, although a general solution has not yet been formulated. The major objective is to identify the particularly important problems of docking with a spinning or tumbling object and present the current status of some promising solutions.