The observations reveal that in many cases loops are not isolated but forming arcades or bundles of loops. In addition there are some observational indications that the single loops are composed by several strands. In both cases it is thus necessary investigate the joint dynamics of the system of several flux tubes. Here we show that the transverse oscillations of several strands can be coupled and the system oscillates with a collective normal mode after an initial disturbance. We study the dependence of the coupling between strands on their relative parameters. We have also considered a multistranded loop model composed of a collection of $N$ parallel strands. We find a huge quantity of normal modes which have a complex structure of the pressure perturbation and velocity field, indicating a strong interaction between the strands. One of the most interesting results of our analysis is that there is no global kink normal mode with all the strands moving in phase and the same direction. Observational implications of these results are discussed.