  Some formulae for the perturbations of the matter fields are summarized
within the framework of the second-order gauge-invariant cosmological
perturbation theory in a four dimensional homogeneous isotropic universe, which
is developed in the papers [K.Nakamura, Prog.Theor.Phys., 117 (2007), 17.]. We
derive the formulae for the perturbations of the energy momentum tensors and
equations of motion for a perfect fluid, an imperfect fluid, and a signle
scalar field, and show that all equations are derived in terms of
gauge-invariant variables without any gauge fixing.
