  A new model of bremsstrahlung emission in the scattering of light nuclei is
constructed with main focus on strict cluster formulation of nuclear processes.
Analysis is performed in frameworks of the folding approximation of the
formalism with participation of $s$-nuclei. Reactions $p$ +$^4$He, $^2$D +
$^4$He, $^3$H + $^4$He, $^3$He + $^4$He are included to analysis. Systematic
analysis of properties of emission of bremsstrahlung photons in the wide region
of kinetic energy of relative motion of two nuclei from 7 to 1000~MeV is
performed. Influence of the oscillator length on the calculated spectra of
bremsstrahlung emission is analyzed. On the example of $^3$H + $^4$He,
dependence of the bremsstrahlung spectra on parameters of nuclear component of
interacting potential is established (at first time for the light nuclei).
Experimental bremsstrahlung data for the proton-deuteron scattering and
proton-$\alpha$-particle scattering are analyzed on the basis of this model.
