  Measurement of the tensor electric and magnetic polarizabilities of the
deuteron is of great interest, especially in connection with the possibilities
of COSY and GSI. These polarizabilities can be measured in storage rings by the
frozen spin method providing a disappearance of g-2 precession. This method
will be used in the planned deuteron electric-dipole-moment experiment in
storage rings. The tensor electric polarizability of the deuteron significantly
influences the buildup of the vertical polarization in the above experiment.
The spin interactions depending on the electric dipole moment, the tensor
electric polarizability, and main systematical errors caused by field
misalignments have very different symmetries. For the considered experimental
conditions, the sensitivity to the deuteron EDM of $1\times10^{-29} e\cdot$cm
corresponds to measuring the both of tensor polarizabilities with an accuracy
of $\delta\alpha_T\approx\delta\beta_T\approx5\times10^{-42}$ cm$^3$. This
conservative estimate can be improved by excluding the systematical error
caused by the field instability which is negligible for the measurement of the
tensor polarizabilities. To find the tensor magnetic polarizability, the
horizontal components of the polarization vector should be measured.
