The subject of this paper is the development and assessment of a new nonlinear parametric identification method for dynamic systems using periodic equilibrium states or outputs. The method consists of a modified Bayesian point estimation technique which can be used in combination with a time discretization method or a shooting method to obtain the periodic equilibrium states. It is assumed that the specific excited and measured periodic solution can be computed directly from a static initial guess. An important feature of this estimator is the possibility to estimate the best parameters based on all experiments of the complete experimental set-up. The choice of using periodic states appears to be computationally efficient compared to using transient states. The new method is applied to multiple sets of nonlinear shaker-test measurements of a uniaxially loaded F-16 nose landing gear damper, for which a standard 1 dof mechanical model and a more comprehensive 2 dof thermo-mechanical model are postulated. Finally, the predictive power of the method is assessed by comparison of predictions for a transient drop-test load case of the 'best' 2 dof model with corresponding parameters and real drop-test measurements.