In this paper, an adaptive self-tuning speed control for a permanent-magnet synchronous motor (PMSM) drive with dead time is proposed. Firstly, to equivalently place the dead time element outside the closed-loop speed control, a dead time compensator (DTC), based on the Smith predictor and a self-tuning proportional-integral model-following controller (ST-PI-MFC) is proposed. The model-following error is used to adaptively update the gains of the ST-PI-MFC via the affine projection algorithm (APA). Secondly, a disturbance observer, based on the time delay control (TDC) approach is used for torque feed forward control. The system's model is greatly simplified when the disturbance observer is combined with the motor. Relying on the simplified model, a natural adaptive observer is used to estimate the motor speed. Unknown motor parameters are estimated by minimizing the state estimation error using an iterative gradient algorithm offered by the affine projection. The estimated parameters are used to update the gains of the integral-proportional (IP) servo loop controller, the disturbance observer and the Smith model. The validity and usefulness of the proposed control scheme are verified through simulation and experimental results.