A combined dynamical and statistical approach to describing induced fission of heavy nuclei is proposed. This approach takes into account the nuclear-dissipation phenomenon and the double-humped structure of the fission barrier. A method that is intended for calculating the angular distribution of fission fragments and which is applicable over a broad range of excitation energies is discussed. The potential of the approach is demonstrated by addressing the problems of self-consistently describing experimental data on fission probabilities for plutonium and americium isotopes, the yields of shape isomers in the α+238U reaction at alpha-particle energies in the range E α = 20–32 MeV and the d+242,240Pu reactions at deuteron energies in the range E d = 20–30 MeV, fission times in the α + 238U reaction at alpha-particle energies in the range E α = 20–32 MeV, and angular distributions of fission fragments in the α + 238U, 237Np reactions at alpha-particle energies in the range E α = 20–100 MeV.