Abstract
This paper presents the existence of. Si'lnikov heteroclinic orbits in the Schimizu-Morioka system and the Zhou system by using the undetermined coefficient method. As a result, the. Si'lnikov criterion along with some technical conditions guarantees that the Schimizu-Morioka and Zhou systems have both Smale horseshoes and horseshoe type of chaos. Moreover, the geometric structures of attractors are determined by these heteroclinic orbits.