By a perturbation treatment of the vibration-rotation Hamiltonian, expressions are derived for the sextic centrifugal distortion constants of a polyatomic molecule in terms of the basic molecular parameters. The calculation can be simplified by reordering the terms in the perturbation expansion. The theoretical expressions for the sextic distortion constants contain the cubic anharmonic potential constants, for which they are a possible source of information. The formulas are applied to molecules of various types of symmetry, and numerical results are computed for sulfur dioxide, ammonia and methane from published anharmonic force fields. The agreement with the observed distortion constants is good for SO 2 and reasonable for NH 3, but poor for CH 4. These results probably reflect the present state of knowledge of the cubic potentials of these three molecules.