We consider a general system of hyperbolic balance laws in m space dimensions (m >= 1). Under a set of conditions we establish the existence of global solutions for the Cauchy problem when initial data are small perturbations of a constant equilibrium state. The proposed assumptions in this paper are different from those in literature for the system. Instead, our assumptions are parallel to those used in the study of hyperbolic-parabolic systems. In one space dimension our assumptions are natural extensions of those used in the study of the Green’s function of the linearized system. They are also sufficient
to the study of large time behavior in the pointwise sense for the nonlinear system, carried out in a different paper.