In this paper, the problems of delay identifiability and delay estimation for a nonlinear systems subject to constant unknown output delay are studied. Usually, the estimation of such delay is based on a monotonic condition which is hard to satisfy in the case of nonlinear systems. To deal with this open and interesting problem, a change of coordinates is introduced in this paper to transform the nonlinear system to the triangular form. Then, a high order sliding mode observer is designed based on implicit Lyapunov function to estimate the state and delayed-input, based on these estimation, the delay estimator is proposed. The convergence of the proposed observer is proved and the effectiveness of the proposed method is illustrated through simulation results of an Electro-Hydraulic Actuator (EHA) system.