We study transverse fast magnetohydrodynamic waves in a system of two coronal loops modeled as smoothed, dense plasma cylinders in a uniform magnetic field. The collective oscillatory properties of the system due to the interaction between the individual loops are investigated from two points of view. First, the frequency and spatial structure of the normal modes are studied. The system supports four trapped normal modes in which the loops move rigidly in the transverse direction. The direction of the motions is either parallel or perpendicular to the plane containing the axes of the loops. Two of these modes correspond to oscillations of the loops in phase, while in the other two they move in antiphase. Thus, these solutions are the generalization of the kink mode of a single cylinder to the double cylinder case. Second, we analyze the time-dependent problem of the excitation of the pair of tubes. We find that depending on the shape and location of the initial disturbance, different normal modes can be excited. The frequencies of normal modes are accurately recovered from the numerical simulations. In some cases, because of the simultaneous excitation of several eigenmodes, the system shows beating.