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This work presents the analysis of the stability of magnetic bimerons in a cylindrical nanotube. Through micromagnetic simulations, we study the influence of magnetic and geometrical parameters on the bimeron existence and size. The obtained results allow us to present diagram states showing the stability region of a bimeron as a function of the nanotube’s height and radius for different anisotropy and Dzyaloshinskii–Moriya interaction strengths. We also obtain two other magnetic states in the range of parameters where the bimeron is not stable: helicoidal and saturated states.