The Josephson relation is generalized for conserved charges in multicomponent bosons. With linear response theory, a formula for derivation of generalized superfluid density is given. When there are several conserved charges, the superfluid density is generally a second-order tensor in internal spin space. When the rank of the Green's function matrix is one, the Josephson relation is given explicitly with a phase operator method. For two-component bosons, a generalized Hugenholtz-Pines relation holds and there exist two gapless phonon excitations. When the interactions are invariant, we show there is a gapless quadratic dispersion excitation no matter how strong the interactions are. The corresponding generalized Josephson relation is expressed with Green's function matrix elements.