In a left near-ring N denote by \(N_ 0\) and \(N_ c\) respectively the zero symmetric and constant parts of N. Call N mixed if neither \(N_ 0\) nor \(N_ c\) is zero. The author investigates near-rings whose additive groups are direct or semidirect sums of subgroups of \(N^+\). He defines three rather special types of semidirect sums called \(\alpha\)-sum, \(\beta\)-sum and \(\gamma\)-sum, whose definitions are too lengthy to include in a brief review. The three main theorems are stated in terms of these special sums. Theorem 1: A mixed near ring N has \(N_ 0\) as a two- sided ideal iff it is isomorphic to an \(\alpha\)-sum of \(N_ 0\) and \(N_ c\); Theorem 2: A zero symmetric near-ring N has \(N^+=I\oplus J\), where I, J are left ideals with trivial intersection iff N is isomorphic to a \(\beta\)-sum of I and J; Theorem 3: A near ring N is a zero-symmetric near-ring with \(N^+=A\oplus B\), where \(A=\{x\in N|\) \(Nx=0\}\) and B is a right ideal without zero divisors iff N is isomorphic to a \(\gamma\)- sum of A and B.