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We consider the partially dissipative hyperbolic systems of balance laws.Under entropy dissipative conditions and [SK] stability condition, we develop a general the ory on the global existence of classical solutions in the framework of Chemin-Lerners spaces with critical regularity.To do this, an elementary fact that indicates the rela tion between homogeneous and inhomogeneous Chemin-Lerners spaces is achieved.Finally, we apply the new result to a specific fluid model-the compressible Euler equations with damping, and obtain the corresponding global existence.