Abstract: The stability of discrete system zero dynamics is not always presented in the sampling process, and it deeply limits the achievable control performance for controller design. To solve this problem, we analyze the representation for discrete-time models and derive the discretization dynamics properties of sampling zero dynamics for a linear discrete-time system corresponding to a continuous-time system with relative degree two in the case of a zero-order hold. More importantly, we also provide approximate expressions of sampling zero dynamics in the form of a power series expansion up to the fourth order term for sampling periods. Meanwhile, the asymptotic behavior of sampling zero dynamics is discussed for small sampling periods and a new stability condition, which is an extension of the previous results, is derived. The condition for ensuring the stability of sampling zero dynamics of the desired linear model is also extended. It assures the stability of sampling zero dynamics in nonlinear control systems.