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This work investigates the free axisymmetric vibrations of a closed spherical nano-shell using the Eringen nonlocal elasticity theory. The motion equations are properly formulated considering the hypotheses of thin shells and the solution is obtained using the classical separation of variables method. The effect of the nonlocal parameter on the natural frequencies and modal shapes are discussed in comparison to their local counterparts. This study could be useful in biomedical and bioengineering applications as well as in other fields related with the nanotechnology.