Abstract: Processes have mereological structure, just like things. Unlike things, however, processes have parts that can be said to ‘emerge,’ in a fairly strong sense of that term.  Since classical mereology does not allow for sums of processes to have any emergent parts ('the whole is not greater than the sum'), we need a non-classical mereology to represent our reasoning about the parts of processes.  In this paper I offer a preliminary sketch of such a mereology. In the first part of this paper I question the (almost) ubiquitous belief that ‘part-of’ in its most basic sense is a transitive relation.  In a second step I sketch the  non-classical mereological system'Leveled Mereology' (LM) which operates with a non-transitive 'is-part' relation and is designed to capture the logical properties of the most general and inferentially weakest part-whole relation: 'belongs-with.'  In a third step I show how claims about the emergent parts of processes can be formulated with the tools of LM.  I conclude with a brief discussion of the significance of this formal presentation.

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