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This work evaluates the influence of initial geometric imperfections on a slender cylindrical panel nonlinear response, considering the three following cases of internal resonances: 1: 1, 1: 3 or 1: 1: 2. Nonlinear Donnell shallow shell theory is used to obtain the nonlinear equations of motion. Based on previous works, a consistent modal solution for the transverse displacement field is derived from a perturbation technique, considering the modal coupling and interaction in a simply supported cylindrical panel. Then, the standard Galerkin method is applied to reduce the problem to a system of differential equations in time domain. The backbone curves, resonance curves, phase-portraits and basin of attraction are obtained to evaluate the influence of the initial geometrical imperfection on the stability of transversally excited circular cylindrical panels. The numerical results indicate that the presence of an initial geometrical imperfection changes strongly the resonance curves, creating news stable paths and dynamic jumps and increases the nonlinearity and complexity of the panel response for each case of internal resonance, leading to fractal basins of attraction in the main resonance region.