We shall treat the most elementary cases : limits of cyclic groups and dihedral groups in the space of finitely generated groups.

For both classes, the solution is surprisingly easy. Indeed, we are able to make a list of the very restricted isomorphism types occuring as limits.

We also characterize these limits in terms of universal theory (sentences in the language of group theory with a single "∃" symbol at the beginning) in the spirit of a theorem of Remeslennikov on limits of free groups.