A full order observer is designed for a class of nonlinear systems that can potentially admit unstable zero dynamics. The structure of the observer is composed of an Extended High Gain Observer (EHGO), for the estimation of the derivatives of the output, augmented with an Extended Kalman Filter for the estimation of the states of the internal dynamics. The EHGO is also utilized to estimate a signal that renders the internal dynamics observable. In the special case of the system being linear in the internal dynamics, we managed to achieve semiglobal asymptotic convergence of the estimation error. We demonstrate the effectiveness of the observer by applying it to a Translating Oscillator with a Rotating Actuator (TORA) system.