This paper studies cooperative tracking problem of heterogeneous Euler-Lagrange systems with an uncertain leader, with emphasis on simultaneous adaptive estimation of the state and parameters of the leader node. The observer design does not rely on the frequency information of the leader node, and the estimation errors are shown to converge to zero exponentially. The results can be applied to general directed graphs, due to two newly developed Lyapunov equations, which solely depend on communication network topologies. Interestingly, using these Lyapunov equations, many results of multi-agent systems over undirected graphs can be extended to general directed graphs. This paper also advances the knowledge base of adaptive control systems by providing a main tool in the analysis of parameter convergence for adaptive observers.