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A multivariable adaptive scheme is proposed that is designed to reject periodic disturbances of unknown frequency at multiple sensor locations. The case of square systems is considered, as well as the common case where there are more sensors than actuators (overdetermined systems). The disturbances are assumed to contain multiple harmonics associated with a single fundamental frequency, as is the case if the source of the disturbances is a rotating machine. Accordingly, the control inputs are selected to be periodic signals with a frequency determined by a single frequency estimate. Although the adaptive scheme is highly nonlinear, approximations yield an analysis that enables a linear time-invariant design of the algorithm. The analysis also gives useful information about the dynamic behavior of the system and the selection of the design parameters. Experimental results show that the proposed scheme is able to significantly reduce acoustic noises with constant or time-varying frequency at multiple locations in an enclosure.