In this paper, the problem of electrical and mechanical parameter estimation in Surface-Mounted Permanent Magnet Synchronous Motors (PMSMs) by means of the Algebraic Identification method is addressed. A complete identification methodology is proposed in two stages: the first stage addresses the identification of the electrical parameters, and the second stage tackles the identification of the mechanical parameters. Both stages are assisted by a model-free observer to estimate the angular speed of the PMSM. Three cases of simulation show that the algebraic identification method provides promising results to identify the electrical and mechanical parameters of the PMSM from the measurement of the currents i <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</inf> , i <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</inf> and the angular position θ.