  We formulate a supersymmetric theory in which both a dilaton and a
second-rank tensor play roles of compensators. The basic off-shell multiplets
are a linear multiplet (B_{\mu\nu}, \chi, \phi) and a vector multiplet (A_\mu,
\l; C_{\mu\nu\rho}), where \phi and B_{\m\n} are respectively a dilaton and a
second-rank tensor. The third-rank tensor C_{\mu\nu\rho} in the vector
multiplet is 'dual' to the conventional D-field with 0 on-shell or 1 off-shell
degree of freedom. The dilaton \phi is absorbed into one longitudinal component
of A_\mu, making it massive. Initially, B_{\mu\nu} has 1 on-shell or 3
off-shell degrees of freedom, but it is absorbed into the longitudinal
components of C_{\mu\nu\rho}. Eventually, C_{\mu\nu\rho} 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.
