  In this paper we study the main properties of the Ces\`aro means of
bi-continuous semigroups, introduced and studied by K\"{u}hnemund in [24]. We
also give some applications to Feller semigroups generated by second-order
elliptic differential operators with unbounded coefficients in $C_b(\R^N)$ and
to evolution operators associated with nonautonomous second-order differential
operators in $C_b(\R^N)$ with time-periodic coefficients.
