[en] Nonlinear evolution of fast ions and Alfven eigenmodes, especially the toroidicity-induced Alfven eigenmodes (TAEs), is investigated with two types of Fokker-Planck-MHD simulations. In the first type of simulation, the fast-ion evolution is described by a 4-dimensional Fokker-Planck equation which takes fast-ion source and slowing down into account. The background plasma is described by the nonlinear full MHD equations. A bursting behavior of multiple TAEs, which takes place in neutral beam injection experiments, is reproduced when the slowing-down time is much longer than the mode damping time and the fast-ion pressure is sufficiently high. In the second type of simulation, 5-dimensional Fokker-Planck equation is solved with a linear TAE. In addition to the particle source and slowing down, the pitch-angle scattering is taken into account. The simulation code is benchmarked with the linear behavior of the alpha-particle-driven n=4 TAE in the TFTR D-T plasma. With a realistic pitch-angle-scattering rate and a chosen damping rate, the relaxation time to a steady saturation state is found to be too long to explain the experiment. (author)