We consider the theory of CCS-Like languages when partial traces (simply finite sequences of actions that the process may perform) are the only observation. We characterize process equivalence, giving relational, logical, and operational definitions and showing that they coincide. This relation is adequate for all languages defined by a class of CCS-like rules; it is fully abstract for any language including process copying and controlled communication poeration. We also give a complete inequational axiom system for this notion of process equivalence for finite processes.