The authors deal with the problem of characterizing the complex and the real stability radii for finite dimensional systems of the form \[ \dot x= (A_0+z_1A_1 +\cdots+z_mA_m)x \] where the uncertain parameters \(z_i\) satisfy \(|z_i|\leq \alpha_i\) \((i=1,\dots,m)\) and the bounds \(\alpha_i\) are known. They consider the following two cases: (1) each \(A_i\) is affected by a structured perturbation \[ A_i+\sum D_{ij} \Delta_{ij}E, \] where the matrices \(D_{ij}\) and \(E\) are known and the matrices \(\Delta_{ij}\) are unknown; (2) each \(A_i\) is affected by an affine perturbation \[ A_i+\sum\delta_{ij}D_{ij}, \] where the matrices \(B_{ij}\) are known and the parameters \(\delta_{ij}\) are unknown. In particular, for case (1), when \(A_0\) is a Metzler matrix (i.e., all the off-diagonal elements are nonnegative) and, in addition, the matrices \(A_i\), \(D_{ij}\) and \(E\) are nonnegative, they prove that the complex radius and the real radius coincide, and characterize it in terms of the norms of the transfer matrices \(G_{ij}=EH^{-1}D_{ij}\). Similar results are given for the case (2). Applications to time delay differential systems are discussed in the last section.