We introduce a new version of expansiveness for flows. Let $M$ be a compact Riemannian manifold without boundary and $X$ be a $C^1$ vector field on $M$ that generates a flow $/varphi_t$ on $M$.  We call $X$ {/it rescaling expansive} on a compact invariant set $/Lambda$ of $X$ if for any $/epsilon>0$ there is $/delta>0$ such that, for any $x,y/in /Lambda$ and any time reparametrization $/theta:/mathbb{R}/to /mathbb{R}$, if $d(/varphi_t(x),/varphi_{/theta(t)}(y))/le /delta/|X(/varphi_t(x))/|$ for all $t/in /mathbb R$, then $/varphi_{/theta(t)}(y)/in /varphi_{[-/epsilon, /epsilon]}(/varphi_t(x))$ for all $t/in /mathbb R$. We prove that every multisingular hyperbolic set (singular hyperbolic set in particular) is rescaling expansive and a converse holds generically. Other definitions of expansiveness of flows and their relationships are also introduced.

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