In previous works, it. was predicted. that electronic and nuclear ring currents in degenerate excited states of atomic and molecular systems persist after: the end Of driven circularly polarized atto- or fenntOseCondlaser pulses On :retain-rely tong time scales, often on pico- or nanosecond time scales, before spontaneous emission occurs. Although this conclusion is true in the center of mass frame, it is not true in the laboratory frame, where the translation has to he considered. In this theoretical work, the analytic formulas for the ring current densities, electric ring currents, mean ring current radii, and induced magnetic fields at the ring center, depending on the translational wavepacket widths, are derived. It shows that the ring currents and the corresponding induced magnetic fields in the laboratbrY. fram persist on shorter timecales due to spreading of translational wavepackets. The electronic ring currents in 2p(+/-) orbitals of the hydrogen-like systems decay on the femtosecond time scale, but the corresponding nuclear ring Currents with giant induced. magnetic fields (far example Up to 0.54 MT for 7Li(2+)) and very small mean ring current radii on the femtometer scale decay on the very.short, zeptoseconcl time scale, according to the Heisenberg uncertainty principle. The theory is also applied to ring currents in many-electron atoms and ions as well as to nuclear ring currents in pseudorotating molecules. For example, in first triply degenerate pseuclorcitational states vertical bar nu(1)l(+/- 1)> of the tetrahedral molecule the OsH4, the ring Currents of the heavy central nucleus Os decay on the attosecond time scale.