Effects of nuclear elastic scattering (NES) on the transport of energetic ions in plasma spheres at densities and temperatures of interest for inertial confinement fusion are investigated on the basis of a linear Boltzmann-Fokker-Planck equation. After presenting the adopted calculational model, numerical results are given for two particular problems: (1) the deposition of 14.7 MeV proton energy in a typical deuterium sphere and (2) the inflight fusion probability for energetic deuterons in a D-T pellet. It is shown that in both cases NES effects are significant. An adequate treatment of the slowing-down process, especially consideration of the transport of NES recoils, is essential for an accurate estimation of the energy deposition and of the fusion probability. Calculations neglecting NES considerably underestimate these quantities.