The double-resonance (DR) Raman process is a signature of all sp2 carbon material and provide fundamental information of the electronic structure and phonon dispersion in graphene, carbon nanotubes and different graphite-type materials. We have performed in this work the study of different DR Raman bands of rhombohedral graphite using five different excitation laser energies and obtained the dispersion of the different DR features by changing the laser energy. Results are compared with those of Bernal graphite and shows that rhombohedral graphite exhibit a richer DR Raman spectrum. For example, the 2D band of rhombohedral graphite is broader and composed by several maxima that exhibit different dispersive behavior. The occurrence of more DR conditions in rhombohedral graphite is ascribed to the fact that the volume of its Brillouin zone (BZ) is twice the volume of the Bernal BZ, allowing thus more channels for the resonance condition. The spectra of the intervalley TO-LA band of rhombohedral graphite, around 2450 cm-1, is also broader and richer in features compared to that of Bernal graphite. Results and analysis of the spectral region 1700-1850 cm-1, where different intravalley processes involving acoustic and optical phonons occurs, are also presented.