We propose a distributed algorithm for the group mutual exclusion problem in a network with no share memory whose members only communicate by messages. The proposed algorithm is composed by two players: groups and processes, groups are passive players while processes are active players. For the coordination access to the resource, each group has assigned a quorum. The groups have associated priorities in each stage, meanwhile the processes have the same level priority. An important feature is that processes have associated a time to participate in the group in each stage.