  In this paper, we have investigated different classes of an AG-groupoid by
their structural properties. We have prove that weakly regular, intra-regular,
right regular, left regular, left quasi regular and completely regular coincide
in an AG-groupoid with left identity and in AG^{**}-groupoid. Further we have
prove that every regular (weakly regular, intra-regular, right regular, left
regular, left quasi regular, completely regular) AG-groupoid with left identity
(AG^{**}-groupoid) is regular but the converse is not true in general. Also it
has been shown that non-associative regular, weakly regular, intra-regular,
right regular, left regular, left quasi regular and completely regular AG^{*}
groupoids do not exist.
