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Recurrent neural networks of the Lotka-Volterra model have been proven to possess characteristics which are desirable in some neural computations. A clear understanding of the dynamical properties of a recurrent neural network is necessary for efficient applications of the network. This paper studies the global convergence of general Lotka-Volterra recurrent neural networks with variable delays. The contributions of this paper are: 1) sufficient conditions are established for lower positive boundedness of the networks; 2) global exponential stability conditions are obtained for the networks. These conditions are totally independent of the variable delays which are therefore allowed to be uncertain; 3) novel Lyapunov functionals are constructed to establish delays dependent conditions for global asymptotic stability, and 4) simulation results and examples are provided to supplement and illustrate the theoretical contributions presented.