The optical mode structure of a Fabry—Perot interferometer-resonator composed of two infinite strip mirrors is investigated from the point of view of the general theory of nonspectral resonances. It is shown that the classical description of this configuration is inadequate to describe its response to highly monochromatic laser radiation and must be supplemented by a discussion of the transverse resonance behavior. This introduces a fine structure to the classical Fabry—Perot rings and implies a discrete resonance behavior for the Fabry—Perot interferometer. In analogy to the characterization of quantum-mechanical virtual levels by wavefunctions and complex energies it is convenient to characterize the discrete resonances of a Fabry—Perot by mode functions and complex resonant frequencies. On the basis of a reformulation and asymptotic expansion of a previously given stationary expression, it is shown that in the high-frequency limit, the open sides of the structure can be replaced by an effective impedance boundary condition. The solution of an elementary resonance problem then yields analytic approximations for the mode shapes, characteristic oscillation frequencies, and modal lifetimes. In the common domain of validity these results are in excellent agreement with previous numerical work on this problem.