  The non--linear dynamics of cosmological perturbations of an irrotational
collisionless fluid is analyzed within General Relativity. Relativistic and
Newtonian solutions are compared, stressing the different role of boundary
conditions in the two theories. Cosmological implications of relativistic
effects, already present at second order in perturbation theory, are studied
and the dynamical role of the magnetic part of the Weyl tensor is elucidated.
