The analysis of internal resonances in continuous structural systems is one of the main research areas in the field of nonlinear dynamics. Internal resonance between two vibration modes occur when the ratio of their natural frequencies in an integer number. Of particular importance, due to its influence on the structural response, is the 1:1 internal resonance, usually associated with system symmetries, the 1:2 internal resonance, due to quadratic nonlinearities, and the 1:3 resonance arising from cubic nonlinearities. The internal resonance enables the energy transfer between the related vibration modes, leading usually to new phenomena with profound influence on the stability of the dynamic response. Shells of revolution usually exhibit internal resonances due to the inherent circumferential symmetry and a dense frequency spectrum in their lower frequency range. This may lead not only to m:n internal resonances, but also multiple internal resonances. In this thesis, the analysis of multiple internal resonances in slender cylindrical shells is conducted, in particular 1:1:1:1 and 1:1:2:2 internal resonances are investigated in detail, a topic rarely found in the technical literature. The investigation of internal resonances in continuous systems is usually conducted using low dimensional discrete models. Although some previous works have investigated m:n internal resonances in cylindrical shells, many results are not consistent since the derived discrete models do not consider the modal couplings due to quadratic and cubic nonlinearities. Here, using a perturbation procedure, consistent modal expansions are derived for an arbitrary number of interacting modes, leading to reliable low dimensional models. The accuracy of these models is corroborated using the Karhunen-Loève method. Finally, it is well known that small geometric imperfections of the order of the shell thickness has a strong influence on the shell nonlinear response. However, their influence on internal resonances, dynamic instability and energy transfer is largely unknown. Thus, the influence of different types of modal imperfection is properly considered in the present analysis. Using the derived discrete models, a detail bifurcation analysis, using continuation techniques and Floquet stability criterion, is presented, clarifying the importance of internal resonances on the nonlinear vibrations and instabilities of cylindrical shells. The results also confirm that the form and magnitude of initial geometric imperfections has a profound influence on the results enabling or preventing the energy transfer among the considered resonant modes.