Abstract: In this paper the qualitative analysis of a class of Lotka-Volterra competition systems with continuous time delays are given. First, we discuss the stabilities of the systems. Then using Hopf's bifurcation theorem and Birkhoffs theorem we show that the delay-induced-instability can lead to appearance of stable limit cycles and that the systems may have recurrent solutions. Finally, some numerical examples are given in order to illustrate the results mentioned above.

Key words: competition system, continuous time delay, bifurcation