Abstarct: Vibration analysis and stability of twisted beam structures have been the subject of research of the many researchers in many fields of engineering and plays an important role in designing the turbine blades, drilling and drilling bits, pumps and ... . Practically, these structures can be modeled as the twisted beams. According to the research, it is clear that there are many cases that have not been investigated by researchers in the field of stability and dynamic behavior of axially twisted beams. One of the most important is that many researches on the dynamic behavior of these beams has focused on their simplified linear equations. Also, there are not nonlinear studies on the vibrational behavior of such beams by considering the unbalance, asymmetry, stretching, in-extensionality, axial speed fluctuation and axial load variations under different boundary conditions. Therefore, in first step, this paper examines the nonlinear dynamic and vibrational behavior of axial twisted beams. In the next steps, the influence of some geometrical factors on this nonlinear investigation such as boundary condition type, axial speed fluctuation, stretching or in-extensionallity, axial loads ,and axial and torsional coupling are investigated. The nonlinear equations of motion have been extracted using Hamilton's principle and the final equations have been obtained with direct method(applying multiple scales method on the partial differential equations) and indirect method(converting the partial differential equations to the ordinary differential equations by the Galerkin method and applying the multiple scales method to the ordinary differential equations). Validation of the results and equations was also performed using the Rang-Kutta numerical method and also compared with the results of other researchers. In these studies, primary and parametric resonances analysis of the system was performed and the effect of various parameters such as twist angle, mode number, longitudinal to transverse stiffeness ratio of the beam, damping ratio, and eccentricity of the beam on the steady state solutions or bifurcations of the symmetrical and asymmetrical twisted beam with above mentioned boundary conditions have been studied.