In this article, we present a novel distributed adaptive output feedback control for the cooperative output regulation problem of linear multiagent systems. The agent plant is general in the sense that those interesting practical issues such as unknown dynamics, directed network graph, and agents with nonidentical relative degrees are taken into account simultaneously. The obtained controller consists of the reduced-order observer, the internal model, as well as the adaptive control law, all of which are shown to be fully distributed without using the knowledge of Laplacian matrix of the network graph. It is of interest to see that, in our recursive design, each agent does not need to estimate the unknown parameters from the neighbors, giving rise to a merely two-dimensional adaptive law with quite a simple structure. It is also this feature that our design has the capability of handling the agents with arbitrary nonidentical high relative degrees.