The focus of the present investigation is on assessing the applicability and performance of the recently introduced Multifidelity Monte Carlo (MFMC) for the computationally efficient prediction of the statistics of the random response of uncertain structures especially those undergoing large deformations and modeled within nonlinear reduced order models. Three such nonlinear applications are considered the first of which is a purely structural problem, a panel subjected to a large loads inducing nonlinear geometric effects. Reduced order models with different fidelities are then generated by reducing the size of the basis from a given set of basis functions. The second nonlinear application is a multiphysics problem, a panel undergoing a simulated high speed trajectory with aerodynamic-structural-thermal coupling. The third application is also multiphysics and focuses on the limit cycle oscillation behavior of a wing past flutter due to structural nonlinearity. In addition, a preliminary validation of the methodology was also carried out that focuses on the linear response of a structure modeled in finite elements where different fidelities are obtained by varying the mesh size. In all of these applications, the MFMC performed very well leading to accurate predictions of the statistics of the response at a reduced/much reduced computational cost.