The present invention provides methods and apparatus for providing access priority in a MAC protocol of a communications system such as, for example, with respect to UMTS RACH. Particularly, the invention introduces several access priority methodologies including: (i) random chip delay access priority (RCDAP); (ii) random backoff based access priority (RBBAP); (iii) variable logical channel based access priority (VLCAP); (iv) UMTS-specific variable logical channel based access priority (VLCAP′); (v) probability based access priority (PBAP); and (vi) retransmission based access priority (REBAP). Each methodology associates some parameter or parameters to access priority classes in order to influence the likelihood of a remote terminal completing a successful access request to a base station.