  Relativistic cosmological perturbation analyses can be made based on several
different fundamental gauge conditions. In the pressureless limit the variables
in certain gauge conditions show the correct Newtonian behaviors. We consider
the general curvature and the cosmological constant in the background medium.
The perturbed density in the comoving gauge, and the perturbed velocity and the
perturbed potential in the zero-shear gauge show the same behavior as the
Newtonian ones in a general scale. Far inside horizon, except for the
uniform-density gauge, density perturbations in all the fundamental gauge
conditions show the correct Newtonian behavior. In this paper we elaborate
these Newtonian correspondences. We also present the relativistic results
considering general pressures in the background and perturbation.
