We introduce a new class of posynomials, called c-orthogonal posynomials, and we consider the corresponding c-orthogonal programs. The treatment of such programs is motivated by the fact that c-orthogonal posynomial programs having a positive degree of difficulty can be solved under weak assumptions, while ''normal" posynomial programs with such a positive degree reduce in general the spectacular power of geometric programming. The optimal value of an unconstrained or constrained c-orthogonal program is equal to the sum of (positive) coefficients of the objectives, respectively. Especially, using the gained results several interesting inequalities can be proved in a simple way.