In this paper the existence and uniqueness theorems are derived for the equation describing a feedback system consisting of a nonlinear element f and a linear element g which involves the Heaviside unit step function and the delta functional and its derivatives. The conditions of the theorems look involved, but are simply expressed in the frequency domain, the locus defined by the Fourier transform of the linear element being used. The essential part of the method in proving the theorems is to transform the distributional equation to an ordinary nonlinear Volterra type integral equation and apply the known theorem on integral equations to the equation obtained by the transformation.