  The gravitational instability of inhomogeneities in the expanding universe is
studied by the relativistic second-order approximation. Using the tetrad
formalism we consider irrotational dust universes and get equations very
similar to those given in the Lagrangian perturbation theory in Newtonian
cosmology. Neglecting the cosmological constant and assuming a flat background
model we give the solutions of the nonlinear dynamics of cosmological
perturbations. We present the complete second-order solutions, which extend and
improve earlier works.
