Hard X-ray radiation (HXR) time-delays have been studied. HXR was recorded during the solar flares using the BATSE spectrometer. The time-delays energy spectra were obtained for 82 flares; thе spectra were classified under three species: decreasing spectra, increasing spectra and U-shaped ones. The spectra were interpreted on the basis of a model of kinetics of accelerated electrons propagating in the flaring loop with the given plasma concentration distribution and magnetic field configuration. The kinetics in question is governed by the processes of Coulomb scattering, reflecting in the converging magnetic field, and with the return current factored in. Solving the time-dependent relativistic Fokker – Planck equation for the given initial conditions allowed to find the time-dependent electron distribution function along the loop. The brightness distribution of the bremsstrahlung of HXR derived from the electron distribution functions was calculated for different photon energies along the flare loop and used to plot the time-delays spectra. The calculated data showed that decreasing time-delays spectra were tractable assuming spaces of electrons acceleration and injection were separated. The distinction between time-delays spectra from the looptop and footpoints was established.