  For general relativistic spacetimes filled with irrotational `dust' a
generalized form of Friedmann's equations for an `effective' expansion factor
$a_D (t)$ of inhomogeneous cosmologies is derived. Contrary to the standard
Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new
equations include the `backreaction effect' of inhomogeneities on the average
expansion of the model. A universal relation between `backreaction' and average
scalar curvature is also given. For cosmologies whose averaged spatial scalar
curvature is proportional to $a_D^{-2}$, the expansion law governing a generic
domain can be found. However, as the general equations show, `backreaction'
acts as to produce average curvature in the course of structure formation, even
when starting with space sections that are spatially flat on average.
