We study the Green's function for a general hyperbolic-parabolic system, including the Navier-Stokes equations for compressible fluids and the equations for magneto hydrodynamics. More generally, we consider general systems under the basic Kawashima Shizuta type of conditions. The first result is to make precise the secondary waves with subscale structure, revealing the nature of coupling of waves pertaining to different characteristic families. The second result is on the continuous differentiability of the Green's function with respect to a small parameter when the coefficients of the system are smooth functions of that parameter. The results significantly improve previous results obtained by the authors. © 2009 Wuhan Institute of Physics and Mathematics.