Absorption of waves propagating across an inhomogenous magnetic field is of crucial importance for cyclotron resonance heating. When the Larmor radius of the resonant particles is small compared to the wavelength then the propagation is described by differential equations, a comparatively simple method for obtaining which has recently been given by Cairns et al. [Phys. Fluids B 3, 2953 (1991)]. In a fusion plasma there may, however, be a significant population of ions whose Larmor radius is not small compared to the wavelength. In this case the system is described by integro-differential equations, reflecting the fact that the plasma response at a given position is determined by the wave field over a region of width of the order of the Larmor radius. The simplified method referred to above is adapted to this case and used to obtain various farms of the equations. Methods of simplifying the equations while still retaining information from the non-local response, are discussed and some illustrated numerical results presented.