The present invention provides a variety of methods for an M2M terminal reporting a power outage when an abnormal power outage occurs, and apparatuses for supporting same. A method for performing a random access procedure for reporting the abnormal power outage in the wireless access system supporting an M2M environment, according to one embodiment of the present invention, comprises the steps of: an M2M device receiving a message comprising an abnormal power outage ranging backoff starting parameter and an abnormal power outage ranging backoff ending parameter, which are used for reporting the abnormal power outage; entering an idle mode; and performing the random access procedure for reporting the abnormal power outage using the abnormal power outage ranging backoff starting parameter and/or the abnormal power outage ranging backoff ending parameter, when the abnormal power outage occurs in the idle mode.