The Carmelies Theory (CT) was successful in Non–Dark Matter explanation of the rotation curves of galaxies. But is this theory also applicable in extragalactic scales or other fields?. In this article, we used this theory for two specific cases (Galaxy Cluster Mass (GCM) and Globular Cluster Velocity Dispersions) and finally (according to the observational data) they have come to the conclusion that the theory is facing problems in these fields.