The oscillation symmetry is first applied to electromagnetic interactions of particles and nuclei. It is shown that the differences between successive masses plotted versus their mean values and the electromagnetic decay widths $\Gamma_{ee}$ of $0^{-}(1^{--})$ $b\bar b$ and $c\bar c$ mesons, plotted versus their masses, agree with such symmetry. Then it is shown that the variation of the energy differences between different levels of several nuclei from $^{8}$Be to $^{20}$Ne, corresponding to given electric or magnetic transitions, display also oscillating behaviours. The electromagnetic widths of the electric and magnetic transitions between excited levels of these nuclei, plotted versus the corresponding differences between energies agree also with this property. The oscillating periods describe also an oscillation, the same for E1, M1, and E2 transitions. It is also the case for the multiplicative factor used $\beta$, and for ratios between these parameters. It is shown that the oscillation symmetry is then applied to atomic energy levels of several neutral atoms from hydrogen up to phosphorus. The data exhibit nice oscillations when plotted in the same way as described before.