This paper investigates the event-triggered distributed predictive control (DPC) problem for multi agent systems subject to bounded disturbances. A novel event-triggering mechanism which involves the neighbours' information is derived for each agent to achieve a trade-off between resource usage and control performance. In such a framework, the DPC optimization problem is solved and information is exchanged only at triggering instants, thus achieving asynchronous coordination. To lower computation and communication consumption more significantly, a dynamic variable considering effects of neighbours is introduced to design a dynamic event-triggering condition and we show that larger inter-execution time can be obtained using the dynamic triggering mechanism. The theoretical conditions on ensuring feasibility and closed-loop stability are developed for these two triggering mechanisms, respectively. Finally, numerical simulations are given to illustrate the effectiveness of the proposed control strategy. (C) 2018 Elsevier Ltd. All rights reserved.