The present invention relates to a wireless access system, and relates to methods for supporting a 256 quadrature amplitude modulation (QAM) modulation mode and devices for supporting the same. In one embodiment of the present invention, the method for supporting a 256QAM in a wireless access system can comprise the steps of: performing, by a terminal, a serving cell adding step of adding a serving cell; receiving, by the terminal, an upper layer signal including a 256QAM indicator for indicating whether a 256QAM is supported in the serving cell; and transmitting and receiving, by the terminal, data by using a first table or a second table according to the 256QAM indicator. At this time, the first table is configured to support a legacy modulation mode, and the second table can be configured to support 256QAM.