We present a garbage-collection algorithm, suitable for loosely-coupled multiprocessor systems, in which the processing elements (PE's) share only the communication medium. The algorithm is global, i.e. it involves all the PE's in the system. It allows space compaction, and it uses a system-wide marking phase to mark all accessible objects where a combination of parallel breadth-first/depth-first strategies is used for tracing the object-graphs according to a decentralized credit mechanism that regulates the number of garbage collection messages in the system. The credit mechanism is crucial for determining the space requirement of the garbage-collection messages. Also a variation of the above algorithm is presented for systems with high locality of reference. It allows each PE to perform first its local garbage collection and only invokes the global garbage collection when the freed space by the local collector is insufficient.