The main objective of this paper is to describe some characteristics of G-AG-groupoids by means of M-systems, P-systems and I-systems. It is proved that if S is a G-AG-groupoid with left identity e, then S is fully prime if and only if every G-ideal is G-idempotent and the set G-ideal (S) is totally ordered under inclusion. Also we show that a left G-ideal Iof G-AG-groupoid S with left identity e is quasi-prime if and only if S/I is an M-system and a left G-ideal Iof a G-AG-groupoid S with left identity e is quasi- G-semiprime if and only if S/Iis a P-system.