The microstructure and pyroelectric properties of AlxGa1-xN composite epitaxial layers grown on SiC/Si(111) and SiC/Si(110) hybrid substrates by the chloride-hydride epitaxy have been studied. The phenomenon of spontaneous formation of a system of heterojunctions consisting of periodic AlxGa1-xN layers of different composition located perpendicular to the direction of growth, was discovered during the growth of layers. Measurements of the pyroelectric coefficients of these heterostructures have shown that regardless of the orientation of the initial Si substrate and their pyroelectric coefficients have close values of the order of γ~(0.7-1)·10-10 C/cm2K. It is shown that to increase the magnitude of the pyroresponse it is necessary to deposit an AlN layer with a thickness exceeding 1 μm on the AlxGa1-xN/SiC/Si surface. This leads to record values of the pyroelectric coefficient γ~18·10-10 C/cm2K for AlN crystals and films. Keywords: silicon carbide-on-silicon substrates, chloride-hydride epitaxy, AlGaN epitaxial layers, aluminum nitride, gallium nitride, pyroelectric properties.