In this chapter, we will cover two standard types of perturbations, namely, bounded perturbations and Miyadera–Voigt perturbations. As a first step towards the perturbation theory for bi-continuous semigroups, we consider bounded perturbations \(B\in \mathscr {L}(X)\) . It will turn out that an additional property of the perturbing operator B is needed. We will establish a positive result on bounded perturbations and investigate their properties. We also give a characterization of semigroups that are “linearly close” to a preliminary given bi-continuous semigroup.