  In this paper we consider nonautonomous elliptic operators ${\mathcal A}$
with nontrivial potential term defined in $I\times\mathbb R^d$, where $I$ is a
right-halfline (possibly $I=\mathbb R$). We prove that we can associate an
evolution operator $(G(t,s))$ with ${\mathcal A}$ in the space of all bounded
and continuous functions on $\mathbb R^d$. We also study the compactness
properties of the operator $G(t,s)$. Finally, we provide sufficient conditions
guaranteeing that each operator $G(t,s)$ preserves the usual $L^p$-spaces and
$C_0(\mathbb R^d)$.
