Thin-walled beams are widely used in aerospace and automobile industry as well as in civil engineering structures. The assessment of local and global stability of thin-walled beams is one of the most important issues in the analysis of thin-walled structures. Our latest research in this field, carried out in the collaboration with the Faculty of Civil Engineering in Subotica, is focused on the problems of global stability of thin-walled beams with asymmetric cross sections. The special attention is paid on the influence of the bimoment induced by axial loads on the bifurcation stability. The existence of the prebuckling bimoment in the equation of torsional stability is recognized by several authors but without numerical evidence of the importance of this term. The lack of interest for this phenomenon could be partially explained by the fact that for all cross sections with at least one axis of symmetry the influence of bimoment on the stability does not exist. Considering analytical models based the Vlasov’s theory and using finite element method we investigated the influence of bimoment on buckling forces and natural frequencies. Eccentrically loaded sections and different boundary conditions are also studied. The investigation of thin walled beams where local buckling and distortion of the cross sections are of interest are in progress.