The paper presents global stability comparative analysis of two distinctive structural systems for one 25 - storey high steel building. These are the system with rigid and the system with hinged joint connections between beams and columns in the steel structure. The analysis focuses on the basic structure which was designed only to carry vertical loads, and on the corresponding structure which was stabilized with vertical bracings in the fa ade walls. Additionally, the paper shows several intermediate steps in the designing of stabilized systems. Static and dynamic design of the relevant structural systems, as well as the control of stress, deformation and stability under the seismic forces of seismic intensity VIII, was done on a computer, on the 3D computation models using Finite Element Method.