Discrete-time models of sampled-data control systems are addressed when both a continuous-time plant and a discrete-time controller have a feedthrough, it is pointed out that in this case discrete-time models which can be found in most references should not be used in the closed-loon context. A new state-space model appropriate for the closed-loop modeling and formulas for calculating the related discrete-time pulse transfer functions are derived, Intersample phenomena are studied and the feasibility of that model to describe systems with parasiting dynamics is emphasized. Examples from the literature illustrate the relevance of the issue.