The Cross beam that is controlled by air-operated valve is a typical two time delays dynamic system involving ~lnknown parameters in engineering. The paper handles a new method to research the stability ofthis system on the basis ofgeneralized Strum theo y. The analysis focuses on the stability switches of the system with increase of the time delay from zero to injinity. The Crossbeam system has two zinhown control paramezers. By the discussion, the paper presents the conditions that these parameters must saris- to make the crossbeam stable in time delay range. It is found that the system undergoes one stability switch as the lime delay increases.