The electromagnetic eigenfrequencies fnsmin a perfectly conducting spheroidal cavity are determined analytically, by a shape perturbation method. The analytical determination is possible in the case of small values of the quantity = 1- a2/b2, (|1), where 2a and 2b are the lengths of the rotation axis and the other axis of the spheroidal cavity, respectively. In this case, exact, closed-form expressions are obtained for the expansion coefficients and in the resulting relation fns(0) [1 + + There is no need for using any spheroidal eigenvectors in our solution. The electromagnetic field is expressed in a series of spherical eigenvectors, while the equation of the spheroidal boundary is given in terms of the spherical coordinates. Numerical results are given for the eigenfrequencies of the lower-order magnetic and electric modes.