Abstract A vibrational analysis has been carried out on cyclohexane, cyclohexane-d12, cyclohexane-1, 1,4,4-d4 and cyclohexane-1,1,2,2,4,4,5,6-d8 utilizing the set of 60 internal coordinates (all 18 bond stretches, all 36 valence angle bends and six CCCC torsional bends) that is compatible with the Snyder and Schachtschneider transferable valence force field for saturated hydrocarbons. Twenty-three of these valence force constants can be defined in the cyclohexane system; all 23 parameters were varied independently to fit 133 assigned fundamental frequencies using the method of least squares and giving a final RMS deviation of 14.68 cm−1. The resulting data are compared with those determined from the original Snyder and Schachtschneider values of the 23 force constants. A numerical method has been devised for determining independent linear combinations of valence force constants in each symmetry block; this permits the selection of an independent subset of valence force constants from a dependent or redundant set when redundant internal coordinates are included.