  We prove the existence of BV solutions for $2\times 2$ system of hyperbolic
balance laws in one space dimension. The flux is assumed to have two genuinely
nonlinear characteristic fields. We consider a general force which may possibly
depend on time and space variable as well. To prove the existence, we assume
the initial data to be small in $L^\infty$. Furthermore, we also study
qualitative behavior for entropy solutions to hyperbolic system of balance
laws.
