Beside near-rings with zero-multiplication or constant multiplication also other near- rings can be considered as near-rings with trivial multiplication. From a structure theoret- ical point of view it is reasonable to consider Kurosh{Amitsur radical classes which contain all near-rings with trivial multiplication. In the present note, continuing the investigations of [2], [4] and [5], we shall characterize the semisimple classes of such radical classes. Our characterizations look clumsier than those in [2], [4] and [5], but we exhibit that exact analogues of the mentioned characterizations cannot be achieved.