  The ``Newtonian'' theory of spatially unbounded, self--gravitating,
pressureless continua in Lagrangian form is reconsidered. Following a review of
the pertinent kinematics, we present alternative formulations of the Lagrangian
evolution equations and establish conditions for the equivalence of the
Lagrangian and Eulerian representations. We then distinguish open models based
on Euclidean space $\R^3$ from closed models based (without loss of generality)
on a flat torus $\T^3$. Using a simple averaging method we show that the
spatially averaged variables of an inhomogeneous toroidal model form a
spatially homogeneous ``background'' model and that the averages of open
models, if they exist at all, in general do not obey the dynamical laws of
homogeneous models. We then specialize to those inhomogeneous toroidal models
whose (unique) backgrounds have a Hubble flow, and derive Lagrangian evolution
equations which govern the (conformally rescaled) displacement of the
inhomogeneous flow with respect to its homogeneous background. Finally, we set
up an iteration scheme and prove that the resulting equations have unique
solutions at any order for given initial data, while for open models there
exist infinitely many different solutions for given data.
