[en] Nonlinear hysteretic behaviors and stiffness changes of a seismic isolator are identified by using a Time Domain System Identification (TDSI) based on the secant stiffness model. A new regularity condition of tangent stiffness used in the current TDSI is proposed instead of that used in the conventional Duhem hysteretic operator. The proposed regularity condition is defined with respect to time while that of Duhem hysteretic operator is defined with respect to displacements and restoring forces. The secant stiffness model for the TDSI is obtained by approximating the tangent stiffness under the proposed regularity condition by the secant stiffness at each time step. A least square method is employed to minimize the difference between the calculated response and measured response for the time domain system identification of the secant stiffness. The regularity condition of the secant stiffness is utilized to alleviate ill-posedness of the TDSI and to yield physically meaningful solutions by means of the regularization technique. An optimal regularization factor determined by Geometric Mean Scheme (GMS) is adopted to yield appropriate regularization effects on the system identification. The validity of the proposed method is presented through two numerical examples