This paper deals with global stabilization and disturbance suppression of a class of nonlinear systems using output feedback. The disturbances generated from a unknown linear exosystem are completely compensated. The order of the exosystem is assumed known and the eigenvalues are distinct. No other assumptions are needed in the control design. This means that the proposed control design is able to completely compensate the disturbances without knowing their amplitudes, frequencies and phases, as long as the number of different frequency components in the disturbances is known. A new formulation of state estimation is introduced to ensure the global stabilization and complete disturbance suppression. Adaptive control technique is used to design an adaptive internal model based on a recently introduced formulation of unknown exosystems and the parameters in the adaptive internal model converge to the actual values, from which the unknown disturbance frequencies can be calculated. In the proposed control design, a number of control coefficients are made adaptive so that the result is global with respect to unknown frequencies in the disturbances.