We propose a novel, operational framework to formally describe the semantics of concurrent programs running within the context of a relaxed memory model. Our framework features a ``temporary store'' where the memory operations issued by the threads are recorded, in program order. A memory model then specifies the conditions under which a pending operation from this sequence is allowed to be globally performed, possibly out of order. The memory model also involves a ``write grain,'' accounting for architectures where a thread may read a write that is not yet globally visible. We illustrate our approach by way of examples, and discuss some extensions. We have build a software simulator allowing us to run litmus tests in our semantics.