A theory of fast wave absorption in a high-beta plasma is given. A reduced, second-order, ordinary differential equation has been used which includes all collisionless electron dissipation mechanisms and ion cyclotron damping over many harmonics. This is relevant to the high-harmonic fast wave heating scheme proposed by Ono [Phys. Plasmas 2, 4075 (1995)]. The parameters appropriate to the National Spherical Tokamak Experiment NSTX [J. Spitzer et al., Fusion Technol. 30, 1337 (1996)] have been used to investigate the absorption characteristics of electrons and ions under high-beta, high-harmonic conditions.