We advocate a Process Archaeology (P-Arch) which explores modes of becoming rather than being. We advance three theoretical postulates we feel will be useful in understanding the process of becoming. And then six temporal propositions, with the latter arranged from the briefest to the longest timescale. We lay down the basic conceptual foundation of our approach using the example of pottery making and we follow the process of creativity in between the hand of the potter and the affordances of clay. This specific creative entanglement of flow and form on a fast bodily timescale provides our grounding metaphor for an archaeology of becoming over the long term. Subsequent propositions provide the basis for exploring issues of longer-term material engagement and change.