Anonymity means that the identity of the user performing a certain action is maintained secret. The protocols for ensuring anonymity often use random mechanisms which can be described probabilistically. The user, on the other hand, may be selected either nondeterministically or probabilistically. We investigate various notions of anonymity, at different levels of strength, for both the cases of probabilistic and nondeterministic users. Key words: Anonymity, Probabilistic Automata, conditional probability.