Аннотация:A new class of singularly perturbed parabolic periodic boundaryvalue problems for Burgers type equations including modular advection is considered. The interior layer type asymptotics anda modification procedure to get asymptotic lower and upper solutions is proposed. Byusing such lower and upper solutions, we prove theexistence of a periodic solutions with an interior layer,estimate the accuracy of its asymptotics and establish the asymptoticstability of this solutions.