We investigate the transverse oscillations of a line-tied multi-stranded coronal loop composed of several parallel cylindrical strands. First, the collective fast normal modes of the loop are found with the T-matrix theory. There is a huge quantity of normal modes with very different frequencies and a complex structure of the associated magnetic pressure perturbation and velocity field. The modes can be classified as bottom, middle, and top according to their frequencies and spatial structure. Second, the temporal evolution of the velocity and magnetic pressure perturbation after an initial disturbance are analyzed. We find complex motions of the strands. The frequency analysis reveals that these motions are a combination of low and high frequency modes. The complexity of the strand motions produces a strong modulation of the whole tube movement. We conclude that the presumed internal fine structure of a loop influences its transverse oscillations and so its transverse dynamics cannot be properly described by those of an equivalent monolithic loop.