Distributed adaptive control is a powerful framework to preserve stability of networked multiagent systems in the presence of uncertainties resulting from, for example, modeling errors, unknown control effectiveness, and perturbed information exchange. However, considering multiagent systems that consist of agents with heterogeneous actuator capabilities, implementation of distributed adaptive control approaches is not a trivial task. This is due to the fact that each agent in this case cannot identically execute given local control laws and this can lead to a poor networked multiagent system performance or even overall instability. To make the first attempt to this challenging problem, we consider a class of uncertain networked multiagent systems with single integrator dynamics in the context of a leader-follower problem and propose a novel distributed adaptive control design procedure for guaranteeing overall stability in the presence of agents having different actuator bandwidths. Specifically, a distributed adaptive control architecture is implemented for agent uncertainties and a hedging method, which modifies ideal reference models of each agent, is utilized to allow for correct adaptation that does not get affected due to the presence of actuator bandwidths. We then analyze the stability of the networked multiagent system and compute the actuator bandwidth limits of each agent using tools from Lyapunov stability and linear matrix inequalities.