The far zone radiation from two types of asymmetrically excited systems is considered. The first is a finite cylinder excited by an electric dipole in the radial direction near the cylinder. The second is a prolate spheroid excited by a narrow belt of electric field around the surface of the spheroid. In both cases the body considered is perfectly conducting and the excitation is not necessarily centered at the midplane of the body. In the case of the finite cylinder excited by a radial dipole, an approximate method is used in which the current on the finite cylinder is taken to be identical with the current which would exist on an infinite cylinder under the same excitation. This approximation is shown to be valid analytically and experimentally if the cylinder is not short. The analytic and experimental results are compared for two cylinder lengths. The turnstile antenna mounted on a finite cylinder is considered analytically and the modification of the radiation by the cylinder is exhibited. In the case of the prolate spheroid excited by a narrow belt of electric field, experimental results are compared to analytic expressions. The differences between the experimental and analytic results are considered. The considerations in obtaining accurate experimental results in both asymmetrically excited systems are discussed.