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. Probabilistic process algebra have been of great help in the development of our setting. Key words: Anonymity, probability, nondeterminism. Anonymity is the property of keeping secret the identity of the user performing a certain action. The need for anonymity may raise in a wide range of situations, like postings on electronic forums, voting, delation, donations, and many others. The protocols for ensuring anonymity often use random mechanisms which can be described probabilistically. This is the case, for example, of the Dining Cryptographers [3], Cro...