This paper describes a solution to the problem of consensus/synchronisation for a general class of networked nonlinear multi-agent systems (MAS) using a distributed control strategy with an event-triggered communications (ETC) mechanism. We consider the case where the dynamics of each agent contain linear and Lipschitz nonlinear terms and the underlying communication graph is directed. The strategy proposed has two important properties: (i) it achieves practical consensus, i.e. the synchronisation error that measures the disagreement among the agents’ states converges to a ball centred at the origin, with a radius that can be made arbitrarily small and (ii) the minimum of the inter-event times for each agent is lower bounded by a strictly positive number, hence Zeno behaviour is excluded. Furthermore, it affords system designers adequate tools to trade off the frequency of communications among agents against the level of performance achieved in MAS consensus/synchronisation. Numerical simulation results are also given.