A simple molecular model for calculating the thermodynamic properties of diatomic molecules and axial hydrogen rotors such as HCO, H2CO, C2H4, and C2H6 has been developed. The model uses a Morse potential for stretching vibrations, and harmonic potentials for bending and torsional vibrations. The effects of anharmonicity, centrifugal stretching, and rotation/vibration interactions are all included. For a Morse oscillator, the results are identical to those of Mayer and Mayer (Statistical Mechanics; Wiley : New York, 1946; Chapter 7) and Pennington and Kobe (J. Chem. Phys. 1954, 22, 1442). No comparable results for axial hydrogen rotors are available. The corrections are proportional to the ratio of the characteristic rotational and vibrational temperatures and increase approximately linearly with temperature. In general, the absolute values of the corrections for axial hydrogen rotors are comparable to, but slightly smaller than, those for heterogeneous diatomic molecules containing hydrogen. At the characteristic vibrational temperature, they are of the order of 1%.