The present invention relates to a random access process in a cellular communications system and to a user equipment (UE) and a NodeB adapted for performing the process. A problem with the random access is that the time slot for receiving a random access request (RA-request) has a long unused guard portion. When the UE transmits the RA-request, the distance to the receiving NodeB is unknown, and the purpose of the guard portion is to accommodate for propagation delay. The disadvantage is the inefficient use of the random access channel which results in long delays for UEs to access the network. The present invention solves the problem with a method in which the UE position is determined and the distance and propagation delay between the UE and NodeB is calculated before the transmission of the RA-request, and the timing of the transmission is advanced by the propagation delay.