The authors consider perturbation theorems for \(R\)-sectorial operators. Let \(A\) be an \(R\)-sectorial operator in a Banach space \(X\). Let \(B\) be a perturbation for \(A\) which is relatively small with respect to \(A\). Then \(A+B\) is also \(R\)-sectorial. This result seems to be a generalization of the Kato-Rellich Theorem and the KLMN-Theorem. It is applied to elliptic operators with measurable coefficients. The highest order coefficients are assumed to be bounded and uniformly continuous. Moreover, the authors also treat perturbations for fractional powers of \(R\)-sectorial operators. The results are applied to pseudodifferential operators, to Schrödinger operators, to higher order elliptic operators and to perturbations by imposing Dirichlet boundary conditions.