Abstract: Studies are carried out on the damped oscillations of composite box beams that are inhomogeneous over the shell thickness. The shell of the box beam forms the outer load-bearing layer made of unidirectional CFRP and an inner vibration-damping layer of stiff elastic material. Two structures for reinforcing the load-bearing layer of the shell of the box beam are considered: symmetric and asymmetric. The influence of orientation of the reinforcement of the load-bearing layer of the shell on the appearance of various types of vibration coupling in inhomogeneous composite box beams is noted. It is established that if the differential equations of natural oscillations contain odd derivatives of the eigenfunctions with respect to the spatial variable (a symmetric beam, bending-bending interaction of an asymmetric beam), then the variation in the reinforcement orientation is accompanied by mutual transformation of the eigenmodes of interacting vibration modes. If the equations contain only even derivatives (longitudinal-torsional interaction of an asymmetric beam), then there arises no mutual transformation of the eigenmodes of interacting vibration modes. It is shown that the dissipative characteristics of composite box beams can be substantially increased by including a vibration-damping layer of “rigid” isotropic viscoelastic material into the composition of their shells. The estimates of the effect of the relative thickness of the vibration-damping layer of the shell and the temperature of the surrounding medium on the values of the eigenfrequencies and the loss factors of coupled vibrations of inhomogeneous box beams are given.