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This study proposes a two-step identification method for estimating the four parameters of a nonlinear model of a position-controlled servomechanism. In the first step, the proposed approach, called the algebraic recursive identification method (ARIM), uses a parametrization derived from the operational calculus currently employed in algebraic identification methods (AIM) recently proposed in the literature. The procedure for obtaining this parametrization eliminates the effect of constant disturbances affecting the servomechanism and filters out the high-frequency measurement noise. A recursive least squares algorithm uses the parametrization for estimating the linear part of the servomechanism model, and allows eliminating the singularity problems found in the AIM. The second step uses the parameters obtained in the first step for computing the Coulomb friction coefficient and the constant disturbance acting on the servomechanism. Experimental results on a laboratory prototype allow comparing the results obtained using the AIM and the ARIM.