The origin of multiple stellar populations in Globular Clusters (GCs) is one of the greatest mysteries of modern stellar astrophysics. N-body simulations suggest that the present-day dynamics of GC stars can constrain the events that occurred at high redshift and led to the formation of multiple populations. Here, we combine multi-band photometry from the Hubble Space Telescope (HST) and ground-based facilities with HST and Gaia Data Release 2 proper motions to investigate the spatial distributions and the motions in the plane of the sky of multiple populations in the type II GCs NGC 5139 ($omega,$Centauri) and NGC 6656 (M 22). We first analyzed stellar populations with different metallicities. Fe-poor and Fe-rich stars in M 22 share similar spatial distributions and rotation patterns and exhibit similar isotropic motions. Similarly, the two main populations with different iron abundance in $omega,$Centauri share similar ellipticities and rotation patterns. When analyzing different radial regions, we find that the rotation amplitude decreases from the center towards the external regions. Fe-poor and Fe-rich stars of $omega,$Centauri are radially anisotropic in the central region and show similar degrees of anisotropy. We also investigate the stellar populations with different light-element abundances and find that their N-rich stars exhibit higher ellipticity than N-poor stars. In $omega,$Centauri Centauri both stellar groups are radially anisotropic. Interestingly, N-rich, Fe-rich stars exhibit different rotation patterns than N-poor stars with similar metallicities. The stellar populations with different nitrogen of M 22 exhibit similar rotation patterns and isotropic motions. We discuss these findings in the context of the formation of multiple populations.
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