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The author deals with adaptive estimation of unknown disturbances in a class of non-minimum phase nonlinear systems, and the stabilisation and disturbance rejection based on the estimated disturbances. The unknown disturbances are the combination of sinusoidal disturbances with unknown frequencies, unknown phases and amplitudes. The only information of the unknown disturbances is the number of distinctive frequencies inside. The class of nonlinear systems considered by the author consists of nonlinear systems in the output feedback form and the systems may be non-minimum phase, that is with unstable zero dynamics. An adaptive estimation algorithm is developed to give exponentially convergent estimates of the unknown disturbance and the system states. The asymptotic convergent estimates of unknown frequencies are also obtained. The proposed estimation algorithm works for both minimum phase and non-minimum phase nonlinear systems in output feedback form. Disturbance rejection with stabilisation is achieved by combining the control designed for the stabilisation of the disturbance-free system and the exponentially convergent estimate of the disturbance. Under the conditions specified for the control design of the system with no disturbance, the overall stability and complete rejection of the unknown disturbance are guaranteed by the proposed control algorithm.