A random access procedure between a mobile terminal and a network is performed based upon the characteristics of a RACH preamble. If the RACH preamble was explicitly signaled by the network, a downlink channel is monitored until a new transmission is indicated according to radio resource allocation information received from the network. If the RACH preamble was not explicitly signaled by the network, a contention resolution timer is started and the downlink channel is monitored until the contention resolution timer expires. Such monitoring of downlink channels in a more efficient manner, results in effective reduction in power consumption.