A study is made on the dynamic stability of thin-walled beams of monosymmetrical cross section. Under the action of axial periodic loads, the parametric excitation of the coupled flexural-torsional type of vibrations is investigated. The nonlinear differential equations and the appropriate boundary conditions used in the analysis of the problem were obtained using the energy formulation. The effect of large angles of rotation and the effect of longitudinal deformations were taken into account. The parametric stability of a thin-walled beam of monosymmetrical split ring section is studied. The study included the establishment of the regions of parametric instability. The steady-state response and the transient growth of the amplitude of oscillations are investigated when the system is parametrically excited. Attention is focused on the response when the coupled flexural-torsional type of vibrations of predominant torsional characteristics is excited. The effect of viscous damping on the steady-state and the transient responses is also included in the analysis.