In this Chapter, a bifurcation tree of period-1 motion to chaosChaos in a flexible nonlinear rotorFlexible nonlinear rotor system is presented through period-1 to period-8 motions. StableStable and unstable periodic motions on the bifurcationBifurcation tree in the flexible rotor system are achieved semi-analytically, and the corresponding stabilityStability and bifurcation of the periodic motions are analyzed by eigenvalueEigenvalue analysis. On the bifurcationBifurcation tree, the appearance and vanishing jumping phenomenaJumping phenomena of periodic motions are generated by saddle-node bifurcationsSaddle-node bifurcation, and quasi-periodic motionsQuasi-periodic motions are induced byNeimark bifurcations Neimark bifurcationsBifurcation. Period-doubling bifurcationsPeriod-doubling bifurcations of periodic motions are for developing cascaded bifurcation treesCascaded bifurcation trees, however, the births of new periodic motions are based on the saddle-node bifurcation. For a better understanding of periodic motions on the bifurcation tree, nonlinear harmonic amplitude characteristics of periodic motions are presented. Numerical simulationsNumerical simulations of periodic motions are performed for verification of semi-analytical predictionsSemi-analytical predictions. From such a study, nonlinear Jeffcott rotor possesses complex periodic motions. Such results can help one detect and control complex motions in rotor systems for industry.