  We propose a multi-field extension of (generalized) G-inflation, based on
covariant multi-galileons and their generalization preserving second-order
field equations. We compute the quadratic action for cosmological
perturbations. By comparing the formulas for cosmological perturbations, it is
highlighted that multi-field DBI galileon inflation is not included in the
multi-field version of generalized G-inflation. Our result indicates that the
generalized covariant multi-galileon theory is not the most general
multi-scalar-tensor theory with second-order field equations.
