We formulate a supersymmetric theory in which both a dilaton and a secondrank tensor play roles of compensators. The basic off-shell multiplets are a linear multiplet (B µν , χ, ϕ) and a vector multiplet (A µ , λ; C µνρ ), where ϕ and B µν are respectively a dilaton and a second-rank tensor. The third-rank tensor C µνρ in the vector multiplet is 'dual' to the conventional D -field with 0 on-shell or 1 off-shell degree of freedom. The dilaton ϕ is absorbed into one longitudinal component of A µ , making it massive. Initially, B µν has 1 on-shell or 3 off-shell degrees of freedom, but it is absorbed into the longitudinal components of C µνρ . Eventually, C µνρ with 0 on-shell or 1 off-shell degree of freedom acquires in total 1 on-shell or 4 off-shell degrees of freedom, turning into a propagating massive field. These basic multiplets are also coupled to chiral multiplets and a supersymmetric Dirac-Born-Infeld action. Some of these results are also reformulated in superspace. The proposed mechanism may well provide a solution to the long-standing puzzle of massless dilatons and second-rank tensors in supersymmetric models inspired by string theory.