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The Cauchy problem for the following system of conservation laws with relaxation time $delta$ is discussed: $(ast)$ $(u+v)_t+f(u)_x=0$, $delta v_t=A(u)-v$. A theorem on the well-posedness of the problem is given in the class of functions with bounded total variation. Then the behaviour of solutions to $(ast)$ as $delta o 0$ is treated and convergence of a certain finite-difference scheme to the so
