  The Josephson relation is generalized for conserved charges in
multi-component 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 Green's function matrix is one, Josephson relation
is given explicitly with phase operator method. For two-component bosons, with
quantum field theory, we show a generalized Hugenholtz-Pines relation hold and
existence of two gapless phonons. When the interactions are $U(2)$ 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.
