The system created in noncentral relativistic nucleus-nucleus collisions possesses large orbital angular momentum. Because of spin-orbit coupling, particles produced in such a system could become globally polarized along the direction of the system angular momentum. We present the results of Lambda and (Lambda) over bar hyperon global polarization measurements in Au+Au collisions at root s(NN)=62.4 and 200 GeV performed with the STAR detector at the BNL Relativistic Heavy Ion Collider (RHIC). The observed global polarization of Lambda and (Lambda) over bar hyperons in the STAR acceptance is co...