  We derive the second order hydrodynamic equations for the relativistic system
of multi-components with multiple conserved currents by generalizing the
Israel-Stewart theory and Grad's moment method. We find that, in addition to
the conventional moment equations, extra moment equations associated with
conserved currents should be introduced to consistently match the number of
equations with that of unknowns and to satisfy the Onsager reciprocal
relations. Consistent expansion of the entropy current leads to constitutive
equations which involve the terms not appearing in the original Israel-Stewart
theory even in the single component limit. We also find several terms which
exhibit thermal diffusion such as Soret and Dufour effects. We finally compare
our results with those of other existing formalisms.
