We study the propagation of nonlinear acoustic waves in a relaxing fluid. First, it is shown how to obtain, from the equations of fluid mechanics, a generalized nonlinear wave equation including relaxation effects and thermoviscous absorption. Then, in the one-dimensional case, this wave equation is reduced to a generalized Burgers' equation including relaxation. We prove the existence of a unique solution for this parabolic equation with nice initial data. When dissipation and relaxation are omitted, the solutions become discontinuous (shock waves). A local study in the neighbourhood of the shocks (blow-up) shows how viscosity and relaxation can absorb the discontinuity. For high amplitude shocks, we obtain a concrete example of points of double concentration: the sonic boom.