Intermodulation products represent a continuing concern to CATV system operators. In most systems, trunk amplifiers are designed to suppress first and second order intermodulation products. As a result, third order intermodulation products are of primary concern, especially with the increasing use of the 5-30MHz band. Due to the large number of frequencies carried by a typical CATV cable and the often indeterminate V-I characteristics of system nonlinearities, the amplitudes and frequencies of the intermodulation products are usually difficult to predict. It is advantageous, therefore, to understand the effects of nonlinearities in CATV systems and to be able to separate the contributions of amplifiers, connectors, taps, etc. in the overall frequency spectrum. In this paper, we consider, theoretically, the generation of intermodulation products at the junction of the seizure screw of the tap and the center conductor of the trunk line. In particular, the terminal response of a branched coaxial line with a nonlinear device located at the branch is discussed. In addition, the frequency spectrum present as a result of the excitation of the nonlinear device by the fundamental frequencies on the line is derived.