The problem of communication constraints for multiagent systems has attracted considerable attention, but there still lacks the result to solve communication constraints between neighbor agents. This significant and practical issue shall be addressed by establishing event-triggered mechanisms between neighbor agents, such that neighbor information can be transmitted only when the preset events are activated. Subsequently, this paper proposes a novel consensus control strategy for nonlinear strict-feedback multiagent systems carrying with triggered mechanisms and uncertain functions. These uncertainties are going to be handled by using radial basis function neural network, whose unknown weight vector can be estimated by only one required adaptive law. The stability of the control algorithm is strictly proved by Lyapunov functional theory, while the boundedness of all the closed-loop signals are guaranteed and the consensus errors are ensured to be exponentially converged to an adjustable domain. Simulation studies eventually present the effectiveness of this method.