The concepts of prime ideals and corresponding radicals play an important role in the study of nearrings. In this paper, we define different prime strong ideals of a seminearring $S$ and study the corresponding prime radicals. In particular, we prove that $P_e=S\mid P_e(S)=S $ is a Kurosh-Amitsur radical class where $P_{e}(S)$ denotes the intersection of equiprime strong ideals of $S$.