A general analysis for the first-order design of the two- conjugate zoom system, which consist of three lenses and has a real or virtual image, is presented. The design formulas are derived. Of two-conjugate zoom systems, we analyze the solution areas in the system parameter diagrams under two particular initial conditions in which the object/image and pupil magnifications of the middle lens are taken to be 1 and -1 or -1 and 1. Two design methods are proposed. Several examples are given to demonstrate the proposed design procedures.