In this paper the duality theory for continuous linear programming problems is extended to problems defined in spaces of -p-times BocHNEB-integrable abstract functions (1 <p< ∞). Two duality theorems are proved, the first one including the existence of a primal optimal solution, the second one the existence of a dual optimal solution. As introduction the paper contains a short survey on results obtained in the field of duality theory for continuous programs, too.