An adaptive algorithm, compensating for unknown multiharmonic disturbance acting on linear objects under conditions of the unavailable state vector with a defined delay in the control channel is proposed. A new approach is proposed for estimating the frequencies of a multiharmonic signal. It is assumed that all parameters of the multiharmonic disturbance are unknown. The task is completed in several steps. First, an observer is constructed based on a frequency estimation scheme. Secondly, stabilization of the state of the object to zero is carried out using feedback based on the predictor. Examples are given to demonstrate the efficiency of the proposed algorithm. Our main contribution is to propose a new scheme for compensating external disturbances for a linear plant and a new approach for estimating the frequencies of a multisinusoidal signal.