Group communications methods and apparatus are described. In particular, methods for granting a mobile device access to a communications resource, e.g., the right to transmit data, associated with a group are described. User requests for the communications resource are suppressed by the corresponding mobile device, for periods during which the communications resource has been granted to another mobile device. A mobile device may store a suppressed user request so that a resource request signal may be transmitted after the communications resource has been released by the mobile device that was previously granted the resource. In this manner requests that cannot be granted are not transmitted, increasing communications efficiency as compared to systems where requests are not suppressed at the mobile devices. A priority scheme is used in some embodiments to determine whether or not a request should be suppressed while another device has been granted the communications resource.