It is known that in a near-ring N the Levitzki radical L(N), that is, the sum of all locally nilpotent ideals, is the intersection of all the prime ideals P in N such that N/P has zero Levitzki radical. The purpose of this note is to prove that L(N) is the intersection of a certain class of prime ideals, called /-prime ideals. Every /-prime ideal P is such that N/P has zero Levitzki radical. We also introduce an /-semi-prime ideal and show that P is an /-semi-prime ideal if and only if N/P has

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... ero Levitzki radical. We get another characterization of the Levitzki radical of the near-ring as the intersection of all the /-semi-prime ideals.