The problem of the collisional evolution of fast-ion guiding centre orbits inmagnetically confined plasmas is analysed in great detail. Regimes where theradial excursion of a particle orbit from a given magnetic surface is largecompared with its minimum distance from the magnetic axis are specificallyaddressed. These non-standard orbits give rise to new interesting effects. Forinstance, the time scale for precessional and bounce motions becomecomparable, which may have important consequences for plasma stability. Inwardorbit drifts and diamagnetic current effects are amplified in the non-standardorbit regime. The neo-classical bootstrap current does not vanish on themagnetic axis, opening the possibility of entirely non-inductive tokamakoperation. Non-standard fast ion orbits could also significantly affect thepower deposition profile of waves in the ion cyclotron range of frequencieslaunched into the plasma for heating purposes. The analysis in this paper isbased on a combination of analytical and numerical methods for the solution ofthe relevant Hamiltonian dynamical system and associated Fokker-Planckequation.