Direct heteroepitaxy of GaAsP and GaP on GaAs and on Si by low-pressure hydride vapor phase epitaxy (HVPE) is investigated as prior studies for photovoltaics and non-linear optics applications. When growing GaAsP on GaAs, it is found that the ambient gas during substrate pre-heating influences the ternary composition as well as the crystalline quality of the subsequent growth. GaAs0.72P0.28 with bandgap energy of 1.76 eV has been achieved, which would be suitable for a top cell in Si tandem solar cell structures. Growth of GaP was investigated on planar GaAs as a prior study for realizing orientation patterned (OP) GaP on OP-GaAs. Threading dislocations caused by the 3.6% lattice mismatch between GaP and GaAs are suppressed by adjusting the GaCl flow, achieving a low full width at half maximum of 146 arcsec for the X-ray diffraction omega scan. Direct heteroepitaxy of GaAsP on Si aiming for achieving a GaAsP/Si dual junction solar cell is demonstrated. The inherent problem of initiating nucleation during the direct heteroepitaxy of III-V on Si by HVPE is overcome by utilizing the vapor mixing approach to grow a low-temperature GaP buffer layer on Si, followed by a GaAsP layer grown by conventional HVPE.