The act-and-wait concept is a recently developed type of controller, which is receiving growing interest because of its promising features with respect to the control of systems with feedback delay. Although most of its advantages have been widely discussed and verified experimentally, a detailed analysis of the nonlinear behavior of this type of controller is still missing. In this paper, we apply the act-and-wait controller to the digital position control of a single-degree-of-freedom system. The analysis shows both the linear stability and the post-bifurcation behavior of the system, comparing the system with a regular proportional-differential controller and with the act-and-wait controller. The performed investigation confirms most of the advantages of the act-and-wait controller, already known in the literature, regarding the enlargement of the stable region and the possibility of achieving deadbeat control, also in the presence of delay. On the other hand it shows some drawbacks of this controller, related to the post-bifurcation behavior, which presents unbounded motions, and to the robustness of the stability, which appears to be limited.