Abstract: In this paper, by using the qualitative method, we study a class of Kolmogorov’s ecological system with prey having constant adding rate, discuss the relative position and the character of the equilibriums, the global stability of the practical equilibriums and give a group of conditions for the boundedness of the solutions, the nonexistence, the existence and the uniqueness of the limit cycle of the system. Most results obtained in papers [1] and [2] are included or generalized.

Key words: ecological system, differential equations, global stability, limit cycle, existence, uniqueness