A semi-commutation system \(S=\) is a semi-Thue system, where X is a finite alphabet and P is a set of production rules of the form xy\(\to yx\) for some x,y\(\in X\), \(x\neq y\). The corresponding semi-commutation is the map which assigns to every set \(R\subseteq X^*\) of words over X the set f(R) of all words over X which can be derived from some member of R by means of the production rules in P. The paper contains two main results: a) If both \(f(R_ 1)\) and \(f(R_ 2)\) are regular then so is \(f(R_ 1R_ 2)\). b) \(f(R^*)\) is regular provided \(R=f(R)\) is regular and for every word \(\omega\) the directed graph \(\Gamma\) (\(\omega)\) is strongly connected, where \(\Gamma\) (\(\omega)\) is defined as follows: vertices are all letters \(x\in X\) occurring in \(\omega\). There is an edge \(x\to y'\) iff \(x\neq y\) and the production rule xy\(\to yx\) does not belong to P.