The authors consider stochastic alpha-particle losses due to the toroidal magnetic field ripple in a tokamak. The fraction of alpha-particle energy losses is calculated for the whole cycle from generation to thermalization. To determine this quantity they solve a two-dimensional (velocity module – angle) kinetic problem describing Coulomb collisions between alpha particles and plasma electrons and ions as well as the stochastic loss of these particles in the τ-approximation. Calculations show that the losses are not very sensitive to changes in plasma temperature and density but depend strongly on the ripple. For 0.3% ripple on the outer circumference of the chamber the fraction of alpha-particle energy losses does not exceed 1%, but for a 1.2% ripple the losses are already 8–10%, while for a further increase in ripple they can rise as high as 50%.