We have shown that an ideal I of an AG-band is prime i ideal (S) is totally ordered; it is prime i it is strongly irreducible. The set of ideals of S form a semilattice structure. We have proved that if a belongs to the centre of S, then S is zero-simple if and only if (Sa)S = S , for every a in S\{0}. Ideal structure in an AG∗ -groupoid S has also been investigated. It has been shown that if I is a minimal right ideal of S then Ia is a minimal left ideal of S , for all a in S. It has been shown also that every ideal of an AG∗ -groupoid S is prime if and only if it is idempotent and ideal (S) is totally ordered.