The zero dynamics is intrinsic system property associated with a given input-output pair. In the design of output tracking controllers, the stability of the zero dynamics of the control plant is usually assumed to be known in advance, and is determined by analyzing the system dynamic equations. With the help of bond graphs and through physical reasoning, a set of rules were proposed in recent research to determine the structure and the stability of the zero dynamics for a narrow class of systems independent of the system dynamic equations. In this paper, a set of rules are proposed to determine the structure of the zero dynamics for general systems and to analyze the stability of the zero dynamics for a broad class of systems independent of the system dynamic equations. The rules establish a connection between this system property and the physical structures, and are useful guidelines on the adjustment of zero dynamics for the purpose of control design.