The Jahn-Teller effect for bound electronic states has been investigated for many decades. In contrast, nothing is known regarding its occurrence for short-lived electronic states. Here we investigate the linear and the quadratic Ecircle timese Jahn-Teller effect for degenerate resonance states with special regard to the complex potential energy surfaces. We find many new phenomena for both the real and imaginary parts of the potential energy surfaces including additional minima and intersections. Possible simplifications of the equations describing the adiabatic potential energy surfaces are discussed. We also briefly investigate other Jahn-Teller effects in linear approximation. The theoretical concepts are exemplified by calculating ab initio data for the degenerate Pi*-type resonance states of the tris(boramethyl)amin anion along two different doubly degenerate vibrational modes. (C) 2004 American Institute of Physics.