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In CDMA cellular communication system power control is one of the most efficient methods to manage the resources, where the main capacity-limiting factor is co-channel interference. In this paper several closed loop power control algorithms are analyzed considering loop delay to cope with random changes of the radio channel and interference. Adaptive algorithms are considered that utilize ideas from self-tuning control systems. The inherent loop delay associated with closed loop power control can be included in the design process. Another problem in closed-loop power control is that extensive control signaling consumes radio resources, and thus the control feedback bandwidth must be limited. To enhance the performance of closed-loop power control in limited-feedback-case is investigated. The performances of the adaptive algorithms are investigated through both analysis and computer simulations, and compared with well-known algorithms from the literature. After proper investigation and analysis it is anticipated that significant performance improvements are achievable with the adaptive algorithms.