  In this paper we study the centralizer of flows and $\mathbb R^d$-actions on
compact Riemannian manifolds. We prove that the centralizer of every $C^\infty$
Komuro-expansive flow with non-ressonant singularities is trivial, meaning it
is the smallest possible, and deduce there exists an open and dense subset of
geometric Lorenz attractors with trivial centralizer. We show that $\mathbb
R^d$-actions obtained as suspension of $\mathbb Z^d$-actions are expansive if
and only if the same holds for the $\mathbb Z^d$-actions. We also show that
homogeneous expansive $\mathbb R^d$-actions have quasi-trivial centralizers,
meaning that it consists of orbit invariant, continuous linear
reparametrizations of the $\mathbb R^d$-action. In particular, homogeneous
Anosov $\mathbb R^d$-actions have quasi-trivial centralizer.
