Summary: In this paper, we study the centralizer of a separating continuous flow without fixed points. We show that if \(M\) is a compact metric space and \(\phi_t:M\to M\) is a separating flow without fixed points, then \(\phi_t\) has a quasi-trivial centralizer, that is, if a continuous flow \(\psi_t\) commutes with \(\phi_t\), then there exists a continuous function \(A: M\to \mathbb{R}\) which is invariant along the orbit of \(\phi_t\) such that \(\psi_t(x)=\phi_{A(x)t}(x)\) holds for all \(x\in M\). We also show that if \(M\) is a compact Riemannian manifold without boundary and \(\Phi_u\) is a homogenous separating \(C^1 \mathbb{R}^m\)-action on \(M\), then \(\Phi_u\) has a quasi-trivial centralizer, that is, if \(\Psi_u\) is a \(\mathbb{R}^{m}\)-action on \(M\) commuting with \(\Phi_u\), then there is a continuous map \(A: M\to \mathcal{M}_{m\times m}(\mathbb{R})\) which is invariant along orbit of \(\Phi_u\) such that \(\Psi_u(x)=\Phi_{A(x)u}(x)\) for all \(x\in M\). These improve Theorem 1 of [M. Oka, Nagoya Math. J. 64, 1–15 (1976; Zbl 0362.58013)] and Theorem 2 of [W. Bonomo et al., Math. Z. 289, No. 3–4, 1059–1088 (2018; Zbl 1397.37020)] respectively.