The aim of this thesis is to explore the influence of nonlinear effects that arise during low-frequency vibration tests of large space reflector antennas. Both stiffness and damping related nonlinearities are investigated. The work focuses on quantifying amplitude-dependent modal parameters using advanced identification techniques that make use of transmissibility measurements. Before being applied to the reflector data, these methods were first validated on numerical models and simpler experimental structures, in order to assess their effectiveness in capturing and characterizing structural nonlinearities. The ultimate objective is to replicate experimental data accurately and enhance prediction of frequency and amplitude down-shifts, therefore contributing to the optimization of vibration testing approaches.