The general kinetic theory of slow-wave electron cyclotron maser (ECM) interaction is presented. Using the Vlasov-Maxwell equations the perturbation inflicted on the electron distribution function by the action of slow hybrid waves is obtained. A general expression for the power transfer between an electron beam of any equilibrium distribution function and the hybrid fields is derived, which can reveal all the interactions that potentially can occur in the system. The effect of the electron guiding-centre drift and the development of a dipole beam current is also considered. To illustrate the physics of the interaction, the theory is applied to the case of a filamentary cold electron beam with exclusively axial initial electron momentum placed on the axis of the system, and expressions for the starting beam current and the frequency pulling due to the beam presence are derived for the case of the slow-wave ECM mechanism. Numerical examples are presented showing that an electron beam with an accelerating voltage of the order of 200 kV to 500 kV can excite oscillations in the cavity in HE(11) mode with starting currents of 10A to 50 A.