The goal of our study is to obtain a precise dynamic model by applying the technique of system identification for the model-based control of a nonlinear robot arm, taking joint-elasticity into consideration. We previously proposed "decoupling identification method" for a planar serial two-link robot arm with elastic-joints caused by the Harmonicdrive reduction gears. First, this paper reviews the decoupling effectiveness of the proposed identification method. This method serves as an extension of the conventional rigid-joint-modelbased identification, and treats the robot arm as a serial two-link two-inertia system with nonlinearity. The main idea of the decoupling method is nonlinear interaction torques between two links are utilized as identification inputs besides motor inputs. The torques can be computed using the rigid-joint-model parameters and link-accelerometer signals, and enable the serial two-link two-inertia system to be divided into two linear one-link systems. Typical multi-input multi-output linear model estimation algorithms can be applied for the identification method. Physical parameters such as motor inertias, link inertias, joint-friction coefficients and joint-spring coefficients of the dynamic model are estimated by applying the coefficient comparison method to the transfer functions of the one-link two-inertia systems. This is a gray-box modeling approach. Second, this paper extends the proposed method to closed-loop identification from open-loop identification. Thus the method is applicable for not only a SCARA (Selective Compliant Assembly Robot Arm) but also a PUMA (Programmable Universal Manipulation Arm) under gravity. Third, this paper unveils the robustness of the decoupling method against estimation errors of coupling-inertia parameters for computing nonlinear interaction torques; these parameters are obtained by the conventional rigid-joint-model-based identification. Several experiments using the planar serial two-link robot arm with elastic-joints are conducted to demonstrate the effectiveness and robustness of the decoupling identification method.