Closed-loop power control is considered as an important component in the management of radio resources in cellular radio systems. The algorithms are typically based on feedback information, which for practical reasons is outdated. These time delays in the system, hamper the performance and might even result in unstable systems. Several power control strategies have been proposed in order to improve the capacity of cellular radio systems, but time delays are usually neglected. Here, time delay compensation is introduced as a means to improve the dynamical behavior of power controlled cellular systems, despite time delays. The improvements are validated both in theory with respect to global convergence and stability and in some illuminating simulations.