A behavioural theory comprises a set of postulates that characterise a particular class of algorithms, an abstract machine model that provably satisfies the postulates, and a proof that all algorithms stipulated by the postulates are captured by the abstract machine model. This article is dedicated to the development of a behavioural theory for random, parallel algorithms. For this first a theory for nondeterministic, parallel algorithms is developed, which captures the case of uniform distribution for the random choices made by the algorithms. This is followed by a discussion how the uniformity could be replaced by arbitrary distributions.