In this paper the problem of simultaneous state and parameter estimation is studied for a class of uncertain nonlinear systems. A discontinuous adaptive sliding-mode observer is proposed based on a discontinuous nonlinear parameter estimation algorithm. It is shown that such an algorithm provides a rate of convergence faster than exponential. Then, the proposed discontinuous parameter estimation algorithm is included in the structure of a sliding-mode state observer providing an ultimate bound for the full estimation error. Some simulation results illustrate the feasibility of the proposed adaptive sliding-mode observer.