Let

$N$ denote a zero-symmetric left near-ring and

$\sigma $ an automorphism of

$N$. An additive endomorphism

$D$ of

$N$ is called a

$\sigma $-derivation if

$D\left(xy\right)=\sigma \left(x\right)D\left(y\right)+D\left(x\right)y$ for all

$x,y\in N$. This paper extends some commutativity results involving derivations, due to the reviewer and

*G. Mason* [Near-rings and near-fields, Proc. Conf., Tübingen/F.R.G. 1985, North-Holland Math. Stud. 137, 31-35 (1987;

Zbl 0619.16024)]. A typical theorem reads as follows: If

$N$ is a 3-prime near-ring admitting a nontrivial

$\sigma $-derivation

$D$ such that

$D\left(x\right)D\left(y\right)=D\left(y\right)D\left(x\right)$ for all

$x,y\in N$, then

$(N,+)$ is Abelian. Moreover, if

$N$ is 2-torsion-free and

$\sigma $ and

$D$ commute, then

$N$ is a commutative ring.