  We define the concept of $N$-expansivity for flows and extend some of the
results already established for discrete dynamics and for $CW$-expansive flows.
We show examples of $N$-expansive flows but not expansive, and examples of
$CW$-expansive flows but not $N$-expansive for any natural number $N$.} We also
define Komuro $N$-expansivity and prove that on compact surfaces it implies
Komuro expansivity.
