In this paper, the consensus problem of third-order heterogeneous platoon under self-triggered and event-triggered scheme is studied. Different and uncertain driveline time constants of vehicles are the main manifestation of the heterogeneity. Based on this heterogeneous platoon, the string stability under the nonlinear distance policy and constant time headway policy are studied. Then, an event-triggered strategy is introduced into the system to save limited communication and computing resources. Continuous communication between vehicles during detecting the event-triggering function is no need under the proposed event-triggered scheme. Furthermore, Taylor formula is used to design a self triggering scheme. Under the proposed self-triggered scheme, triggering interval is calculated directly by the information of last triggering-instant. Therefore, the Zeno behavior and the continuously detecting of event-triggering function can be avoided. Finally, the effectiveness of the theoretical results is verified by simulations.