  We derive hydrodynamic-like equations that are applicable to short-time scale
color phenomena in the quark-gluon plasma. The equations are solved in the
linear response approximation, and the gluon polarization tensor is derived. As
an application, we study the collective modes in a two-stream system and find
plasma instabilities when the fluid velocity is larger than the speed of sound
in the plasma. The chromo-hydrodynamic approach, discussed here in detail,
should be considered as simpler over other approaches and well-designed for
numerical studies of the dynamics of an unstable quark-gluon plasma.
