This paper is devoted to the global output-feedback stabilisation for a class of nonlinear systems with inherent nonlinearities and coarse disturbance. Remarkably, the disturbance may be non-periodic, non-differentiable and/or of unknown magnitude, and hence some critical requirements on the disturbance in the existing related literature are successfully removed. Recognising that the strategies of disturbance compensation, such as internal model principle, sliding mode control method, learning method and active disturbance rejection control method, are quite hard or even impossible to apply, a time-varying design scheme is developed in the paper. Moreover, the serious unknowns and time-variations reflected in the growth rate of the system are also dealt with by the proposed scheme. By designing a time-varying output-feedback controller, all the signals of the resulting closed-loop system are globally bounded, and the original system state and the observer state ultimately converge to zero.