  In this paper we have discusses {\Gamma}-left, {\Gamma}-right, {\Gamma}-bi-,
{\Gamma}-quasi-, {\Gamma}-interior and {\Gamma}-ideals in
{\Gamma}-AG^{**}-groupoids and regular {\Gamma}-AG^{**}-groupoids. Moreover we
have proved that the set of {\Gamma}-ideals in a regular
{\Gamma}-AG^{**}-groupoid form a semilattice structure. Also we have
characterized a regular {\Gamma}-AG^{**}-groupoid in terms of left ideals.
