Let \(R\) be an integral domain with quotient field \(K\) and assume that \(M\) is a unitary torsion-free \(R\)-module. Following the paper [\textit{J. Moghaderi} and \textit{R. Nekooei}, Int. Electron. J. Algebra 8, 18--29 (2010; Zbl 1257.13002)] the authors call \(M\) a valuation module if for each \(0\neq x\in K\), either \(xM\subseteq M\) or \(x^{-1}M\subseteq M\). Note that in this case \(R_v=\{x\in K|xM\subseteq M\}\) is a valuation overring of \(R\) and \(M\) is an \(R\)-module. Hence \(M\) is a valuation module if and only if there is a valuation overring \(R_v\) of \(R\) contained in \(K\) such that \(M\) is an \(R_v\)-module. Now assume that \(v:K\to \Gamma \cup\{\infty\}\) is a valuation on \(K\) where \(\Gamma\) is an ordered group and let \(0\neq V\) be a \(K\)-vector space. The authors call a function \(\mu:V\to \Gamma \cup\{\infty\}\) a valuation of \(V\) (corresponding to \(v\)), if all of the following conditions hold: \(\mu(x)=\infty\) if and only if \(x=0\); \(\mu(ax)=v(a)+\mu(x)\) for every \(a\in K, x\in V\); \(\mu(x+y)\geq \min\{\mu(x),\mu(y)\}\) for every \(x,y\in V\). This generalizes valuations of fields. The authors prove that if \(\mu\) is a valuation of \(V\), then \(M_\mu=\{x\in V|\mu(x)\geq 0\}\) is a valuation module over \(R_v\), where \(R_v\) is the valuation ring of \(v\). They also present some conditions under which the converse of this statement is true, but they show that there are valuation modules which are not of the form \(M_\mu\) for any valuation \(\mu\) of any \(K\)-vector space.