A continuum theory to describe equilibrium and nonequilibrium solvation in polarizable, nondipolar, quadrupolar solvents is developed. By employing the densities of the solvent quadrupole and induced dipole moments as primary field variables, a reaction field theory formulation for quadrupolar solvents is constructed with account of their electronic polarizability. Nonequilibrium solvation aspects are effected via the solvent coordinate description for the quadrupole moment density. It is found that the theory is consistent with the macroscopic Maxwell equations and satisfies the continuity of the electric potential across the cavity boundaries. Solvation stabilization arising from the solvent quadrupoles is captured via novel reaction field factors analogous to those for dipolar solvents. Comparison is made with the dielectric continuum description of the polarizable, dipolar solvents as well as with previous theories of the quadrupolar solvents. Extensions and applications of the current theoretical formulation to study free energetics and dynamics of reactive and spectroscopic processes in the quadrupolar solvents are reported in the following paper [J. Jeon and H. J. Kim, J. Chem. Phys. 119, 8626 (2003)]. (C) 2003 American Institute of Physics.