This work presents a new theory of multipactor under multi-carrier signals for parallel-plate geometries. It is the generalization of the non-stationary multipactor theory for single-carrier signals1. It is valid for multicarrier signals with an arbitrary number of carriers with different amplitude, arbitrary frequency and phase conditions and for any material coating. This new theory is able to model the real dynamics of the electrons during the multipactor discharge, for both single and double surface interactions. Among other parameters of the discharge, it calculates the evolution in time of the charge growth, electron absorption and creation rates as well as the instantaneous SEY and order. An extensive set of numerical tests with a PIC software has been carried out in order to validate the theory under many different conditions. This theoretical development constitutes the first multipactor theory which completely characterizes the multipactor discharge for arbitrary multi-carrier signals, setting the first step for further investigations in the field.