This paper reviews some of the author's results about the following problem. Consider an equation of the form \[ \chi(z,a_1,\dots, a_m)= 0\tag{1} \] in the complex plane, where \(a_1,\dots, a_m\) are parameters. Let \(D(0)\) be the region of the parameter space for which all the solutions of (1) lie in a preassigned region \(G\) of the complex plane. Let be \((a^*_1,\dots, a^*_m)\in D(0)\). The problem is to find the maximal distance \(\rho^*\) such that for each choice of \((a_1,\dots, a_m)\) with \[ \rho= (\sum\kappa^{- m}_s|a_s- a^*_s|^m)^{{1\over m}}< \rho^* \] the solutions of (1) still lie in \(G\). The author distinguishes the case where (1) depends linearly and the case where (1) depends nonlinearly on the parameters. Several possibilities for \(m\) are considered.