Thermo-acoustic instabilities are dynamic phenomena that represent a major threat for most modern combustion systems. Many studies, mainly undertaking a linear analysis of experimental data, have been carried out to provide a deeper understanding of the underlying phenomena. However, linear analysis may lead to an oversimplified view of the problem, which involves many complex non-linear interactions, and a more detailed non-linear analysis may be necessary. This paper presents both linear and non-linear analyses of experimental measurements observed in a methane-fuelled laboratory combustor. The linear analysis aims to verify the existence of thermo-acoustic instabilities and consists of the elaboration of both power-spectral density distribution and Rayleigh Index of the experimental time series. Nonlinear analysis aims to investigate dynamic behaviours by means of the deterministic chaos theory. Results of the analyses show that combustion instabilities occur in all the experimental operating conditions. Moreover, the existence of a chaotic source in the combustion system under study is demonstrated.