A near-ring \(N\) is called \(N\)-simple if it has no proper \(N\)-subgroups; it is called \(A\)-simple if it has no \(N\)-subgroups \(H\) such that \(HN=\{0\}\). The radical \(J_ 2(N)\) of a zero-symmetric ring \(N\) with an invariant series whose factors are \(N\)-simple is nilpotent; moreover the factor \(N/J_ 2(N)\) is a direct sum of \(A\)-simple strongly monogenic near-rings (a result of Artin-Noether type). For near-rings having an invariant series whose factors are of prime order a characterisation of nilpotence is given, and a link between the nilpotency index and the length of the series, too.