This paper deals with methods for parameter estimation of two-mass mechanical systems in electric drives. Estimates of mechanical parameters are needed in the startup of a drive for automatic tuning of model-based speed and position controllers. A discrete-time output error (OE) model is applied to parameter estimation. The resulting pulse-transfer function is transformed into a continuous-time transfer function, and parameters of the two-mass system model are analytically solved from the coefficients of this transfer function. An open-loop identification setup and two closed-speed-loop identification setups (direct and indirect) are designed and experimentally compared. The experiments are carried out at nonzero speed, making the closed-loop identification setup easier to apply. It was found out that all the identification setups are applicable for the parameter estimation of two-mass mechanical systems.