Software transactional memory (STM) is a concurrency con-trol mechanism for shared memory systems. It is opposite to the lockbased mechanism, as it allows multiple processes to access the same setof variables in a concurrent way. Then according to the used policy, theeffect of accessing to shared variables can be committed (hence, madepermanent) or undone. In this paper, we define a formal framework fordescribing STMs and show how with a minor variation of the rules it ispossible to model two common policies for STM: reader preference andwriter preference.