Abstract: The present invention relates to methods of controlling transmitting power in a cellular radio communication system comprising one or several base stations each communicating with mobile terminals located within its respective area of coverage in which method the desired power change is calculated by means of an adaptive algorithm. Power drift between the desired output power and actually used output power is reduced by making the algorithm reduce the influence of the previously used output power by multiplying it with a “forgetting function” &lgr; with values between 0 and 1. At the receiving end is a decision made whether the received power order commands are reliable or not by checking the soft value of the power order commands. This proposed power control algorithm provides a delta-modulated fast power control method which is robust to errors in the signalling channel and at the same time reacts quickly to fast fading variations.