Let \((T(t))_{t\geq 0}\) and \((S(t))_{t\geq 0}\) be strongly continuous one-parameter semigroups on a Banach lattice E. If \(| T(t)f| \leq S(t)| f|\) for all \(f\in E\) and \(t\geq 0\), one says that the semigroup \((T(t))_{t\geq 0}\) is dominated by \((S(t))_{t\geq 0}\) (which necessarily consists of positive operators). The main concern of the authors’ is the existence of a minimal dominating semigroup for a given semigroup \((T(t))_{t\geq 0}\), which is called the modulus of \((T(t))_{t\geq 0}\). They prove, in particular, that if the semigroup is dominated and the underlying Banach lattice has order continuous norm, then the modulus exists.