The invention relates to the initiation of a service to a mobile terminal capable of communicating via at least a first and second access network. Further, the invention relates to a reduction of power consumption of mobile terminals supporting connectivity to at least two access networks. The invention also relates to mobile communication systems and in particular to mobile communications through heterogeneous access networks. In order to prove improved method for initiating services to mobile terminals and/or to reduce power consumption of mobile terminals, the invention introduces of a sleep state that can be entered by the terminal for an access system if same is not used. Upon requesting a service from/to the mobile terminal, the mobile terminal starts service initiation through a second access system and transits back to active state for the first access system for service provision.