We present multiphase period-colour/amplitude-colour/period-luminosity relations using the Optical Gravitational Lensing Experiment III (OGLE III) and Galactic Cepheid data and compare with state of the art theoretical pulsation models. Using this new way to compare models and observations, we find convincing evidence that both period-colour and period-luminosity relations as a function of phase are dynamic and highly non-linear at certain pulsation phases. We extend this to a multiphase Wesenheit function and find the same result. Hence our results cannot be due to reddening errors. We present statistical tests and movies depicting the period-colour/period-luminosity and Wesenheit relations as a function of phase for the Large Magellanic Cloud (LMC) OGLE III Cepheid data: these tests and movies clearly demonstrate non-linearity as a function of phase and offer a new window towards a deeper understanding of stellar pulsation. When comparing with models, we find that the models also predict this non-linearity in both period-colour and period-luminosity planes. The models with (Z = 0.004, Y = 0.25) fare better in mimicking the LMC Cepheid relations, particularly at longer periods, though the models predict systematically higher amplitudes than the observations.
