Analytic gradient techniques in conjunction withdegenerate perturbation theory are used to analyze theenergetics and the derivative couplings in the vicinity of a conicalintersection. The precision of the analyticgradient based evaluation of the derivative couplings in the vicinityof a conical intersection is established.An approach for the rigorous treatment of two-dimensionalJahn-Teller problems in the absence ofC3v symmetryis suggested.