For a zero-symmetric 3-prime near-ring N, we study three kinds of conditions: (a) conditions involving two derivations d1, d2 which imply that d1 = 0 or d2 = 0; (b) conditions involving derivations which force (N, +) to be abelian or N to be a commutative ring; (c) the condition that dn (S) is multiplicatively central for some derivation d and subset S of N.