  We study continuity and H\"older continuity of $t\mapsto P_tf$, where $P_t$
is a generalized Mehler semigroup in $C_b(X)$, the space of the continuous and
bounded functions from a Banach space $X$ to $R$, and $f\in C_b(X)$. The
generators $L$ of such semigroups are realizations of a class of differential
and pseudo-differential operators, both in finite and in infinite dimension.
Examples of operators $L$ to which this theory is applicable include
Ornstein-Uhlenbeck operators with fractional diffusion in finite dimension, and
Ornstein-Uhlenbeck operators with associated strong-Feller semigroups, in
infinite dimension.
