Process-algebraic languages offer a rich set of structuring techniques and concurrencypa tterns which allow one to decompose complex systems into concurrently interacting simpler component processes. Theyab stract however almost entirely from a notion of system state. The method of Abstract State Machines (ASMs) offers powerful abstraction and refinement techniques for specifying system dynamics based upon a most general notion of structured state. The evolutions of the state are governed however bya fixed and typically unstructured program, called ‘rule’, which describes a set of abstract updates occurring simultaneously at each step (synchronous parallelism). We propose to incorporate into one machine concept the advantages offered byb oth structuring techniques, and introduce to this purpose Abstract State Processes (ASPs), i.e. evolving processes (extended ASM programs which are structured and evolve like process-algebraic behaviour expressions) operating on evolving abstract states the wayt raditional ASM rules do.