PCT No. PCT/FI95/00082 Sec. 371 Date Aug. 19, 1995 Sec. 102(e) Date Aug. 19, 1996 PCT Filed Feb. 17, 1996 PCT Pub. No. WO95/24102 PCT Pub. Date Sep. 8, 1995The invention relates to a method for transmitting calls of different priorities in a cellular network which comprises in each cell at least one base station (10) communicating with subscriber terminals (11a-11d, 13) within its area, and in which network the base station transmits power control information to the terminal equipments, which may adjust their transmit power on the basis of the power control messages from the base station, the calls of the network having different levels of priority. In order to ensure the call establishment and the quality of calls with a high priority, the calls with a high priority use a higher transmit power than what is allowed for calls with a lower priority.