A variational principle for studying one-dimensional wave propagation and damping near the ion-ion hybrid conversion region in a tokamak is presented. In its variational form, the wave equation is closely related to the power balance equation: substituting the electric field for the test function in it yields the generalized Poynting theorem. The guiding centre position rather than that of the particle is adopted as the independent variable. Toroidal and oblique incidence effects are retained but the poloidal magnetic field is neglected. A strictly positive power density for Maxwellian plasmas is ensured by starting from a general formalism due to Lamalle (Lamalle P U 1993 Phys. Lett. 175A 45; 1997 Plasma Phys. Control. Fusion 39 1409) and expanding the operator acting on the electric field in the expression for the absorbed power per guiding centre orbit (rather than expanding the dielectric tensor, as is usually done) in terms of the assumed small parameter , where is the perpendicular wavenumber and the Larmor radius. The general formulae for the dielectric response are provided and explicit expressions are given for the case where up to second-order corrections in are retained in the operator. As an illustration, the absorption of radio frequency power in a (H)-D-(Ar) TEXTOR plasma typical for the radiative improved mode is discussed.