Designing quiet cars has become an important issue in the automotive industry, where passive and active noise control techniques can be employed to improve the acoustic comfort without compromising the vehicle performance. At the design stage of a noise control system, the estimation of the structure-borne sound pressure levels in the car cabin is a challenging problem, as uncertainties in a physical structural-acoustic system have an impact on the vehicle dynamics at high frequencies. Additionally, the response of the system can be affected by nonlinearities in the vibrations transmission path. Therefore, this research has been focused in developing computationally efficient vibro-acoustic models to predict the statistical structural-acoustic response of a system to random inputs, as well as analysing the degree of dependency of the response to nonlinear behaviour in the interface between the excitation and the structure. Key aspects of the impact that a nonlinear transmission path might have in the response of a statistical structural-acoustic system, were investigated from an equivalent damper model of the structural vibrating subsystem, under the assumption of weak acoustic coupling and the infinite plate theory. Numerical data in the time domain were generated from the simplified nonlinear system excited by random inputs with known power spectral density. The effects of nonlinearities were observed and quantified in the power spectral density of the response, as well as in the reduction of coherence between the input and output. Additionally, the Wiener theory in the frequency domain has been explored to estimate the degree of contribution of a nonlinearity of second order to the total response of the system. Finally, an extended hybrid Finite Element-Statistical Energy Analysis (FE-SEA) model was proposed to analyse the response of a deterministic-statistic structural-acoustic system, where the nonlinear transmission path is considered as a deterministic structure. The equations of an existing FE-SEA approach, based on the diffuse field reciprocity, have been generalised to include prescribed displacements as inputs, in addition to external forces. The nonlinear analysis with the FE-SEA approach has been carried out by adopting the concept of equivalent linearisation of the deterministic dynamic stiffness matrix, and the capability of the approach has been validated against experimental data from a physical nonlinear structural-acoustic setup.