Using the second-order Jahn-Teller effect as a basis of calculation, the stable structures of molecules XYn are predicted for n = 2-7. The symmetry argument is used that (ѱ,|εU|Q|ѱk) is nonzero only if the direct product of the representations of ѱ0 and ѱk contains the representation of (εU|εQ). Only the lowest lying one or two excited states are considered forѱk• In spite of this severe approximation, the results are remarkably good for a large variety of molecules and complex ions. The method provides a good test for molecular orbital calculations. © 1969, American Chemical Society. All rights reserved.