The present invention provides various methods and an apparatuses for supporting a group delegator (GD) in a wireless access system supporting Machine to Machine (M2M) communication. A method for selecting the group delegator (GD) in a wireless access system supporting the Machine to Machine (M2M) communication, according to one embodiment of the present invention, comprises the steps of: an M2M device belonging to an M2M group receiving a broadcasting message including a first critical value, which is used for selecting the GD; an M2M device generating a first random value, which is used for selecting the GD; and selecting the GD by comparing the first critical value and the first random value.