The invention relates to an improved method and arrangement for controlling a cell change performed by a terminal of a cellular radio system. In particular the invention relates to a cell change in a situation where the terminal is connected to a special service provided by its current cell, e.g. to the GPRS service (General Packet Radio Service). An essential idea of the invention is that in conjunction with a cell change order a base station sends to the terminal information about whether the terminal is allowed not to carry out the cell change order if the terminal does not know the timing information of the new cell assigned to it. This information is advantageously sent in a signalling message of a certain service, such as the GPRS service. It is an advantage of the invention that a terminal connected to a certain service will not make unnecessary cell change attempts which are doomed to fail. The invention helps direct the cell change in such a manner that the load caused by possible repeated cell change attempts on the terminal and radio signalling is low.