Continuous-time linear programs (CLP) were formulated by Bellman in 1953. Duality theory for CLP and its sub-classes has been studied by several authors. However, duality results for Bellman CLP problems obtained so far are still fairly limiting. We consider a generalization of CLP where solutions reside in the space of functions of bounded variation. We formulate a symmetric dual problem and show that under Slater-type conditions both primal and dual problems possess optimal solutions and there is no duality gap.