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We consider strong travelling wave profiles for a class of 2 × 2 viscous conservation laws. Our main assumption is that the product of nondiagonal elements within the Fŕechet derivative (Jacobian) of the flux is nonnegative. By using the regularization method improved by the author, we prove the existence of strong travelling wave profiles for those systems.doi:10.1090/s0033-569x-2012-01301-0 fatcat:qdjouu7fyzcztoy2atxathcwka