In this paper, we introduce the notion of prime and

semiprime ideal and characterize prime and semiprime 

ideals in a $\Gamma$-seminear-ring.

Among them, for any $\Gamma$-seminear-ring, 

an ideal is semiprime if and only if it is the

intersection of all primes containg it. Moreover, 

an ideal of a $\Gamma$-seminear-ring is prime 

if and only if it is semiprime and strongly 

irreducible.