The ripple transport of fast (suprathermal) ions and electrons in tokamaks is investigated. This transport, which is due to the drift motion of particles blocked in the ripple of a magnetic field, is of the convective type for particles with an energy exceeding some value d. For ions in real tokamaks, this energy region may be close to the bulk of ions having thermal energy. Kinetic equations for the particle distribution function are derived, the ripple drift motion through the magnetic surfaces being taken into account. In the low-energy (diffusive) limit, the results agree with the well-known ones. For more energetic particles convective transport dominates. In particular, a replacement, through the ripple channel, of fast electrons from the hot periphery is possible, resulting there in a considerable rise of the distribution function tail. The increase in the ripple depth from the chamber centre to the periphery is very important; it causes collisionless adiabatic capture of particles by ripples, which are held there, then drift and finally escape from the plasma. This process leads to the formation of a special type of trajectories ('open' trajectories) , which directly connect the chamber walls with the central position of the plasma column and may bring about considerable particle and energy losses. In addition, this phenomenon leads to a depletion of the particle distribution function.