Abstract: The stability of traveling wave solutions to a class of Lotka-Volterra competitive systems with age structures was studied. In the case of quasi-monotonicity, the existence and comparison theorems for the solutions to the initial value problems of the systems were first established on R with the analytic semigroup theory and the abstract functional differential equations. Then based on the weighted energy method, the comparison theorem as well as the embedding theorem, the global exponential stability of the monostable large-speed traveling wave solutions under the so-called large initial perturbation (i.e. the initial perturbation around the traveling wave decaying exponentially as x→-∞,but being arbitrarily large at other locations) was obtained for the systems in the weighted Sobolev space. The results show that, as the steady state solution of the system, the traveling wave solution usually determines the long-term asymptotic behavior of the solution to the initial value problem. Its stability reveals that the phenomena and results of inter-species competition systems can be clearly observed without interference by external factors.