We study the large time behavior in L1 of the compressible, isentropic, viscous 1-D flow. Under the assumption that the initial data are smooth and small, we show that the solutions are approximated by the solutions of a parabolic system, and in turn by diffusion waves, which are solutions of Burgers equations. Decay rates in L1 are obtained. Our method is based on the study of pointwise properties in the physical space of the fundamental solution to the linearized system. © 1994 John Wiley & Sons, Inc.