The influence of nonlinear damping on the dynamics of a generalized Beck’s beam is investigated. A variational principle provides the equations of motion of the system. Bifurcation points are detected via a linear stability analysis. Starting from Hopf’s bifurcation points, a post-critical analysis, based on the Method of Multiple Scales, is directly performed on the continuous system, revealing the double nature of nonlinear damping, which can be beneficial or detrimental in terms of stable or unstable bifurcated equilibria. It is found that both the internal and external nonlinear damping forms can turn super-critical limit cycles into sub-critical ones, thus revealing another destabilizing effect of damping, beyond the very well-known one occurring in the linear field. The results of numerical analyses based on a Galerkin’s discretization of the system confirm the analytical findings.