  The Lagrangian perturbation theory on Friedman-Lemaitre cosmologies
investigated and solved up to the second order in earlier papers (Buchert 1992,
Buchert \& Ehlers 1993) is evaluated up to the third order. On its basis a
model for non-linear clustering applicable to the modeling of large-scale
structure in the Universe for generic initial conditions is formulated. A
truncated model is proposed which represents the ``main body'' of the
perturbation sequence in the early non-linear regime by neglecting all
gravitational sources which describe interaction of the perturbations. However,
I also give the irrotational solutions generated by the interaction terms to
the third order, which induce vorticity in Lagrangian space. The consequences
and applicability of the solutions are put into perspective. In particular, the
model presented enables the study of previrialization effects in gravitational
clustering and the onset of non-dissipative gravitational turbulence within the
cluster environment.
