The authors present a theory of fast-ion transport and fast-ion plasma heating in tokamaks with sawtooth oscillations. The theory is valid for ions with orbit widths that are small compared with the region in which the oscillations occur. It is shown (a) that a sawtooth crash leads to the ejection from the central plasma region of particles with a peaked radial distribution, and (b) that the fast-ion distribution function and the radial plasma heating profile strongly depend on the ratio of the sawtooth oscillation period to the time of Coulomb slowing down of fast ions. The results obtained in this theory are in agreement with neutral injection experiments at JET, where changes in neutron yield have been observed during internal disruptions. However, the comparison of theory and experiment must be regarded as preliminary owing to uncertainties in the database and the simplified theoretical model. The effect of sawtooth oscillations on alpha -particles in a reactor such as ITER is also considered