Equilibrium structures, harmonic vibrational frequencies, and relative energies of 12 neutral or ionic gallium phosphorus hydrides are reported and analyzed. Hartree-Fock (HF), Becke's three-parameter exchange with Lee, Yang, and Parr correlation DFT (B3LYP), and second-order Moller-Plesset (MP2) calculations using the 6-311++G(d,p) basis set were performed on all molecules. Gallium-phosphorus bond energies were determined based on the MP2/6-311++G(d,p) calculations of the equilibrium structures and of their decomposition products. We find that the gallium-phosphorus double bond is, perhaps, surprisingly strong (i.e., 93 +/- 2 kcal/mol) and short (2.128 +/- 0.018 Angstrom); CCSD(T)/6-311 ++G(3df,3dp) single-point calculations on HGaPH corroborate the prediction of a strong double bond. Bond order analysis of some of the neutral species revealed that these compounds satisfy a Pauling relation between bond length and bond order, and also bond energy and bond order. CASSCF(8\8) calculations on H2PGa show that the surprising weakness of the phosphorus-gallium bond in this compound can be understood in terms of an occupied antibonding a orbital. Comparisons of the B3LYP method to NF and MP2 methods reveal that the B3LYP DFT method, in most cases, gives relative energies and equilibrium structures in substantial agreement with the MP2 method for these types of compounds.