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This paper describes a method for the identication and the tracking of poles of a weakly nonlinear structure from its free responses. This method is based on a model of multi-channel damped sines whose parameters evolve over time. Their variations are approximated in discrete time by a nonlinear state space model. States are recursively estimated by a new method which couples a two-pass Bayesian estimator with an Expectation-Maximization (EM) algorithm. An iterative procedure between them allows an accurate and robust tracking of poles. As a result, equivalent modal parameters such as frequency and damping are obtained as a function of amplitudes. The method is applied on numerical and experimental cases and show promising results.