We present a generalized formulation of the Optimized Effective Potential
(OEP) approach to the Self Interaction Correction (SIC) problem in Time
Dependent (TD) Density Functional Theory (DFT). The formulation relies on the
introduction of a double set of single electron orbitals. It allows the
derivation of a generalized Slater approximation to the full OEP formulation,
which extends the domain of validity of the standard Slater approximation. We
discuss both formal aspects and practical applications of the new formalism and
give illustrations in cluster and molecules. The new formalism provides a
valuable ansatz to more elaborate (and computationally very demanding) full TD
OEP and full TD SIC calculations especially in the linear domain
