During the last decade, the existence of nonlinear behaviour in spacecraft dynamic testing was frequently attested. However, current practice in industry is still to ignore nonlinearities, arguably because their analysis is regarded as impractical. The objective of the present contribution is to show that there now exists experimental and numerical methodologies which can deal with nonlinear phenomena in real-life structures. Specifically, this study investigates nonlinear modal interactions evidenced during the qualification campaign of the SmallSat spacecraft developed by EADS-Astrium. The ability to understand and reliably predict such interactions is of utmost importance as they may involve energy transfer between modes and, in turn, jeopardise the structural integrity. The paper proceeds in two steps, leading to great-fidelity reproductions of the experimental observations. In the first step, sine-sweep data collected during the qualification campaign are exploited to build a nonlinear computational model of the SmallSat with good predictive capabilities. To this end, the complete progression through nonlinearity detection, characterisation and parameter estimation is carried out by means of several techniques, such as the wavelet transform and the restoring force surface method. In the second step, the computational model is exploited through continuation algorithms to compute the nonlinear normal modes of the spacecraft and predict potential interactions. A very good agreement between experimental and numerical results is obtained for 2:1 interactions between modes with non-commensurate linear frequencies.