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Nanoscale spheres have led to a growing interest in their potential applications in a wide range of technological fields. Hollow nanospheres can be modelled as closed spherical shells in the analysis of their mechanical behaviour, the ratio of thickness to radius being used to ascertain the pertinence of considering only membrane forces, or both membrane forces and bending moments. Nonlocal elasticity theory has been widely used to analyze the mechanical behaviour of nanostructures. This paper investigates the free axisymmetric vibration of nanoscale spherical shells accounting for both types of internal force, by extending the Kirchhoff-Love plate theory to Eringen nonlocal elasticity theory. The influence of coupled size and bending effects on the frequencies and modal shapes is studied, revealing specific features that cannot be observed in an uncoupled analysis. This study could be useful in biomedical and bioengineering applications as well as in other fields related to nanotechnology.