Abstract: The bilevel-programming problems are important in mathematical applications.
They are usually solved by various kinds of numerical methods. This will give
solutions in the form of local extremal values but not necessarily global optimal ones. Consider the case for which all functions occurred in the bilevel-programming problems are polynomial ones. The present paper shows how to solve the problems by the MM-method (Mathematics-Mechanization method) or Wu's method. Wu's method is different from the numerical methods in that the computations are symbolic instead of numerical ones. Theoretically it is based on computer algebra and algebraic geometry. The author uses the computer to get complete blobal solutions of some practical test problems
in the bilevel-programming. The computations show that Wu's method furnishes the true optimal values of the bilevel-programming problems, and is also quite efficient.

Key words: Wu''s Method, Bilevel-programming, Mathematics mechanization, Characteristic Set, Wsolve