  We discuss the non-linear evolution of the angular momentum L acquired by
protostructures, like protogalaxies and protoclusters, due to tidal
interactions with the surrounding matter inhomogeneities. The primordial
density distribution is assumed to be Gaussian and the non-linear dynamics of
the collisionless mass fluid is followed using Lagrangian perturbation theory.
For a Cold Dark Matter spectrum, the inclusion of the leading-order Lagrangian
correction terms results in a value of the rms ensemble average <L^2>^{1/2}
which is only a factor of 1.3 higher than the corresponding linear estimate,
irrespective of the scale. Consequently, the predictions of linear theory are
rather accurate in quantifying the evolution of the angular momentum of
protostructures before collapse sets in. In the Einstein-de Sitter universe,
the initial torque is a good estimate for the tidal torque over the whole
period during which the object is spun up.
