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In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection - diffusion second order ordinary differential equations subject to the mixed type boundary conditions. We prove that the method has almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and also the numerical derivative are established. Numerical results are provided to illustrate the theoretical results. First published online: 24 Oct 2013