Effects of nuclear elastic scattering (NES) on the slowing down of charged fusion products in a typical deuterium plasma and the burn dynamics of ignited Cat-D and D-D-3He plasmas are investigated on the basis of a linear Boltzmann-Fokker-Planck equation. A multigroup method is used to obtain the distribution functions for the fusion products and their recoils. It is shown that an adequate treatment of the slowing-down process, especially the consideration of NES and of the slowing-down time delay, is essential for an accurate prediction of the dynamic behaviour and the thermal instability of plasmas. NES enhances the thermal instability and accelerates the temperature excursion from the equilibrium. The inclusion of NES results in a 20-30 keV increase in the critical temperature for thermal stability.