The electromagnetic eigenfrequencies fnsmin a perfectly conducting spheroidal cavity are determined analytically. The analytical determination is possible in the case of small values of h = d/(2a), (h « 1), where d is the interfocal distance of the spheroidal cavity and 2a the length of its rotation axis. In this case exact, closed-form expressions are obtained for the expansion coefficients g(2)nsmand g(4)nsmin the resulting relation fnsm(h) = fns(0) [1 + h2g(2)nsm+ h4g(4)nsm+ O(h6)]. Analogous expressions are obtained with the use of the parameter v = 1- a2/b2(for |v| << 1) , where 2b is the length of the other axis of the spheroidal cavity. The electromagnetic field is expressed in terms of spheroidal eigenvectors. Numerical results are given for the lower-order modes.