The interaction of monochromatic Alfven waves with toroidally trapped particles in the intrinsic stochasticity regime is discussed. Both the diffusion in velocities as well as in the radial position of bananas is studied. Using suitable Hamiltonian formalism, the effect of wave parallel component E/sub /// is investigated. By means of the direct numerical integration of the corresponding canonical equations, the stochasticity threshold both for plasma electrons and for thermonuclear alpha-particles is estimated (neglecting the effect of B/sub ///). Stochasticity causes the transfer between trapped and untrapped regimes and the induced diffusion of bananas. The latter effect can exceed the neoclassical diffusion considerably. The effect of B/sub /// has been estimated analytically. It consists in the frequency modulation of banana periodic motion, coupled with the possibility of the Mathieu instability. Nevertheless, for B/sub /// corresponding to E/sub ///, the effect seems to be weaker than the effect of E/sub ///, when thermonuclear regime is considered.