At first the authors give a conception of structural stability for a one-parametric optimization problem. I n the second part there are proved some interesting theorems on convexity intervals, which partially are of importance for the numerical computation of these intervals. At last the method of THEIL and VAN DE PANNE is modified in such a manner, that they get a decomposition of the given convexity interval into stability regions. I n the caae of non-degeneration this decomposition is unique.