  We consider a particular class of Garside groups, which we call circular
groups. We mainly prove that roots are unique up to conjugacy in circular
groups. This allows us to completely classify these groups up to isomorphism.
As a consequence, we obtain the uniqueness of roots up to conjugacy in complex
braid groups of rank 2.
  We also consider a generalization of circular groups, called hosohedral-type
groups. These groups are defined using circular groups, and a procedure called
the Delta-product, which we study in generality. We also study the uniqueness
of roots up to conjugacy in hosohedral-type groups.
