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This paper presents a new approach to rejection of complex-valued sinusoidal disturbances acting at the output of a discrete-time stable linear plant with unknown and possibly time-varying dynamics. It is assumed that both the instantaneous frequency of the sinusoidal disturbance and its amplitude may be slowly varying with time and that the output signal is contaminated with wideband measurement noise. It is not assumed that a reference signal, correlated with the disturbance, is available. The proposed disturbance rejection algorithm is an extension of the algorithm derived for the constant-known-frequency case, described in Part I of this paper.