The work presented in this paper is based on an existing comprehensive formulation for rotating #exible systems. In the existing formulation the #exible degrees of freedom (d.o.f.) are represented by an analytically computed modal basis and the coupling matrices between the rigid-and the #exible-body d.o.f. are developed based on the analytical modal representation of the #exible d.o.f. In this paper, the existing formulation is generalized for rotating beams by representing the #exible d.o.f. either as physical d.o.f. of a "nite element formulation or as a set of retained and internal d.o.f. of a Craig}Bampton formulation. The coupling matrices between the rigid-body rotation and the #exible d.o.f. are developed accordingly. The non-linear e!ects from the work done by the centrifugal forces are included in the formulation. Finite element shape functions of a beam element in a three-dimensional space and "nite element shape functions for solid elements are employed for deriving the coupling terms between the rigid-body d.o.f. and the physical d.o.f. An additional transformation is required and performed when the right-body d.o.f. are coupled with the internal and the retained d.o.f. of a Craig}Bampton formulation. The coupled system of equations is solved in the time domain by combining the Newmark method for time integration and the Newton}Raphson method for solving the non-linear system of equations within each time step. Analyses are performed for a #exible rotating beam in order to validate the development. An analytical solution is compared with the new formulations that represent the rotating beam #exibility with the physical d.o.f. of beam or solid elements. The analytical solution is also compared to the formulation that represents the #exible d.o.f. in terms of retained and internal d.o.f. of a Craig}Bampton formulation. Very good correlation between the analytical and numerical results is observed.