This paper focuses on transient characteristics of natural gas flow in the coordinated scheduling of security-constrained electricity and natural gas infrastructures. The paper takes into account the slow transient process in the natural gas transmission systems. Considering their transient characteristics, natural gas transmission systems are modeled as a set of partial differential equations (PDEs) and algebraic equations. An implicit finite difference method is applied to approximate PDEs by difference equations. The coordinated scheduling of electricity and natural gas systems is described as a bi-level programming formulation from the independent system operator's viewpoint. The objective of the upper-level problem is to minimize the operating cost of electric power systems while the natural gas scheduling optimization problem is nested within the lower-level problem. Numerical examples are presented to verify the effectiveness of the proposed solution and to compare the solutions for steady-state and transient models of natural gas transmission systems.