  We establish the maximal regularity for nonautonomous Ornstein-Uhlenbeck
operators in $L^p$-spaces with respect to a family of invariant measures, where
$p\in (1,+\infty)$. This result follows from the maximal $L^p$-regularity for a
class of elliptic operators with unbounded, time-dependent drift coefficients
and potentials acting on $L^p(\R^N)$ with Lebesgue measure.
