  We prove that sectional-hyperbolic attracting sets for $C^1$ vector fields
are robustly expansive (under an open technical condition of strong dissipative
for higher codimensional cases). This extends known results of expansiveness
for singular-hyperbolic attractors in $3$-flows even in this low dimensional
setting. We deduce some converse results taking advantage of recent progress in
the study of star vector fields: a robustly transitive attractor is
sectional-hyperbolic if, and only if, it is robustly expansive. In a low
dimensional setting, we show that an attracting set of a $3$-flow is
singular-hyperbolic if, and only if, it is robustly chaotic (robustly sensitive
to initial conditions).
