It is demonstrated that the complex acoustic eigenfrequencies of impenetrable spheroids correspond to the phase matching of repeatedly circumnavigating surface waves. Here, the phase matching condition must be formulated in the integral form, since the surface wave propagation constants vary during the passage of the waves over a surface with variable curvature, depending to first order on the local curvature along the path. Using the expressions for the propagation constants obtained by Franz and Galle [Z. Naturforsch. 10a, 374 (1955)], it is possible to satisfy this phase matching condition and, simultaneously, to obtain an indication of the correctness of the complex eigenfrequencies as found from a T-matrix calculation, or from a calculation employing spheroidal functions [D’Archangelo, J. Acoust. Soc. Am. 77, 6 (1985)].