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We prove that in the infinite speed-of-light limit (i.e., non-relativisticand subhorizon limits), the relativistic fully nonlinear cosmologicalperturbation equations in two gauge conditions, the zero-shear gauge and theuniform-expansion gauge, exactly reproduce the Newtonian hydrodynamicperturbation equations in the cosmological background; as a consequence, in thesame two gauge conditions, the Newtonian hydrodynamic equations are exactlyrecovered in the Minkowsky background.

Newtonian limit of fully nonlinear cosmological perturbations in Einstein's gravity