The present invention relates to a wireless access system supporting a millimeter wave (mmWave), and provides methods for performing a fast fallback in order to avoid a link disconnection and devices supporting the same. As an embodiment of the present invention, a method for performing a fast fallback by a terminal in a wireless access system supporting a millimeter wave (mmWave) may comprise the steps of: establishing radio resource control (RRC) connections with a mmWave base station and a legacy base station, respectively; receiving downlink data transmitted from the mmWave base station; receiving, from the legacy base station, resource-related information associated with a resource to be allocated for a fast fallback; detecting whether a non-light of sight (NLoS) transition occurs in a mmWave link with the mmWave base station; and when the NLoS transition occurs, transmitting a fallback request message to the legacy base station in order to perform the fast fallback.