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Increasing interest in coherent PM and FM communication systems using phase-locked demodulators has promoted the development of practical coherent diversity combining systems. Phase-locked loops can convert each received signal of a diversity system to an essentially constant frequency and phase for coherent combination prior to demodulation. When the individual signals are fading with some amount of independence, the properly combined signal has less severe amplitude fluctuations than either signal alone and a diversity improvement results. While practical systems of this type have proved very effective, they have a disadvantage in that each of the phase-locked loops are controlled by the individually fading signals. This paper describes a multiple-input servosystem in which a primary phase-locked loop is controlled by the combined signal while auxiliary loops within the primary loop assure phase coherence. In this way, the full diversity improvement is realized in both locking and in demodulation and the probability of losing lock is correspondingly decreased. The probability of a single-input phase-locked loop losing lock is established and then extended to the case of a slowly fading signal with Rayleigh envelope characteristics. The statistics of two such signals optimally combined are used to arrive at a comparative estimate of the improvement possible. A practical diversity-locked combiner is analyzed and design criteria are established.