We present a semiclassical analysis of resonance states supported by a conical potential well coupled to a conical peak. The positions of the energy levels are calculated by Wentzel-Kramers-Brillouin (WKB) procedures, which are applied to an adiabatic Hamiltonian with the contribution from the geometric phase taken into account. The probability of escape from the well is calculated by resorting to a comparison equation of the Zener-Dykhne-Chaplik type. The widths of the energy levels are calculated via the escape probability by using a general relation derived recently by Zhu, Nikitin, and Nakamura [J. Chem. Phys. 104, 7059 (1996)]. It is shown that the present calculations are in excellent agreement with accurate numerical data for the positions and widths as recovered from an analysis of the scattering matrix and from a direct calculation of the complex-valued energy levels. The results obtained explain the very fast decay of the low-lying states and the good performance of the surface-hopping approximation. (C) 1997 American Institute of Physics. [S0021-9606(97)02139-9].