The paper presents a method to estimate the speed and the rotor position of the permanent magnet synchronous motor (PMSM) drive. The development is done using sliding mode theory. The method proposed is based on the model of the PMSM in the stationary reference frame and uses two sliding mode (SM) observers to estimate the variables of interest: the states, the rotor position and the motor speed. A distinct advantage of the proposed approach is that speed is obtained algebraically - some previous speed estimation methods described in the state of the art use adaptation theory; however, this is usually not reliable. In the development, the motor voltages and currents are measured. A first SM observer estimates the EMFs of the PMSM model. Then, these are fed into a second SM observer which estimates the derivatives of the EMFs. The equivalent controls of the two observers are used to compute the speed. The paper discusses some of the approaches available to estimate the speed with known EMFs. The theoretical developments are supported with simulations.