Investigation of the two-dimensional problem of the excitation of a circular cylinder with a surface impedance that varies along the circumference. The integral equation for the surface density of the electric or magnetic current is solved numerically by the I<rylov-Bogolyubov method. Results of calculations of the current distribution and radiation patterns are presented for two laws of variation of the impedance and several values of the curvature of the surface upon excitation of the cylinder by a slot. Curved impedance surfaces are of considerable interest in connection with the design of surface wave antennas and bends in transmission lines with surface waves. It is known that in such cases energy carried by the surface wave is radiated as a result of the curvature of the surface and the inhomogeneity of the impedance. A number of authors have investigated surface waves traveling over a curved surface (see, for example, [1-8]). However, they have generally been concerned with the case of small curvature and constant surface impedance. In [3] Felsen considered the excitation of a circular cylinder with a surface impedance modulated in accordance with a sinusoidal law, but with a small percentage modulation. In practice, especially in the design of surface wave antermas, particular importance attaches to the case of pronounced curvature and arbitrary, including aperiodic, variation of impedance. This paper is devoted to consideration of a method of designing systems with variable surface impedance located on a circular cylinder. 1. The Integral Equation Consider the following problem: an infinite impedance cylinder of radius a is excited by external electric and magnetic currents located in a region S. I shall employ the cylindrical coordinate system r, ~o, z, making the z axis coincide with the axis of the cylinder, and confine the examination to the two-dimensional problem, assuming that the distribution of the external sources and the surface impedance does not depend on the z coordinate. Suppose the external sources create a field corresponding to an H-wave relative to the cylinder axis, i.e., only the field components E r, Er H z are nonzero. Then the external electric and magnetic currents may be represented by the following components of the current volume density vector: jEre, jE~ jzMe. Electric and magnetic surface currents I E and I M are induced on the cylinder and the boundary condition