  Newtonian cosmological perturbation equations valid to full nonlinear order
are well known in the literature. Assuming the absence of the
transverse-tracefree part of the metric, we present the general relativistic
counterpart valid to full nonlinear order. The relativistic equations are
presented without taking the slicing (temporal gauge) condition. The equations
do have the proper Newtonian and first post-Newtonian limits. We also present
the relativistic pressure correction terms in the Newtonian hydrodynamic
equations.
