When dealing with the design or with the application of any technical system, which is not quite simple and trivial, one has to face to the problem to determine the allowable de viations of the system functions and the optimal vector of system parameter tolerances. The need for the solution of this problem is stimulated with various serious economic and maite nance aspects, between them the tendency to reach the minimal production cost, the maximal system operation reliability are the most frequent. Suppose that we are dealing with an system S, consisting of N components represented by the system parame ters xi' i = 1, 2. N, which are arranged in certain structu re so, that the K, system functions F k' k = 1, 2. IG, expres sing the considered system properties, fullfil the condition F-FO~ AF, /1/ \'Ihere F = l F k} Ie is the set of the actual system functions, FO = lFOk}~ is the set of the nominal system functions and A F = l A F k 1(;. } is the set 0 f the a 11 0 w a b 1 e s emf y s t u n c ion t s de viations. The set F depends besides the system structure also on the vector X = [Xi}N of the system parameters. Suppose, that the system structure is invariant.