This paper presents a Bayesian model updating and model class selection approach based on nonlinear normal modes (NNMs). The performance of the proposed approach is demonstrated on a conceptually simple wing-engine structure. Control-based continuation is exploited to measure experimentally the NNMs of the structure by tracking the phase quadrature condition between the structural response and single input excitation. A two-phase Bayesian model updating framework is implemented to estimate the joint posterior distribution of unknown model parameters: (1) at phase I, the effective Young’s modulus of a detailed linear finite element model and its estimation uncertainty are inferred from the data; (2) at phase II, a reduced-order model is obtained from the updated linear model using Craig-Bampton method, and coefficient parameters of structural nonlinearities are updated using the measured NNMs. Five different model classes representing different nonlinear functions are investigated, and their Bayesian evidence are compared to reveal the most plausible model. The obtained model is used to predict NNMs by propagating uncertainties of parameters and error function. Good agreement is observed between model-predicted and experimentally identified NNMs, which verifies the effectiveness of the proposed approach for nonlinear model updating and model class selection.