Context: We present the CoRoT light curve of the β Cep star HD 180642, assembled during the first long run of the space mission, as well as archival single-band photometry. Aims: Our goal is to analyse the detailed behaviour present in the light curve and interpret it in terms of excited-mode frequencies. Methods: After describing the noise properties in detail, we use various time series analyses and fitting techniques to model the CoRoT light curve, for various physical assumptions. We apply statistical goodness-of-fit criteria that allow us to select the most appropriate physical model fit to the data. Results: We conclude that the light-curve model based on nonlinear resonant frequency and phase locking provides the best representation of the data. Interpretation of the residuals is dependent on the chosen physical model used to prewhiten the data. Conclusions: Our observational results constitute a fruitful starting point for detailed seismic stellar modelling of this large-amplitude and evolved β Cep star. The CoRoT space mission was developed and is operated by the French space agency CNES, with participation of ESA's RSSD and Science Programmes, Austria, Belgium, Brazil, Germany, and Spain. Appendix A is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/506/111 Postdoctoral Fellow of the Fund for Scientific Research, Flanders.