The author introduced and investigated strict Markovian marked closed random sets (CRS) which are the special case of marked closed random sets considered earlier, see the foregoing review, Zbl 0575.60012. Let \((\nu_ t,\zeta_ t)\in \{1,...,m\}\times {\mathbb{R}}_+\) be a subordinator in a random environment that is strict a Markovian right continuous process with left limits for which \(\zeta_ 0=0\), component \(\zeta_ t\) increases and has jumps at the moments of \(\nu_ t\)-jumps. Let also \({\mathcal M}^ 0_ m\) be the family of collections of closed mutually disjoint subsets \((M_{(1)},...,M_{(m)})\) of \({\mathbb{R}}_+\) for which \(O\in \cup M_{(i)}\). The main result is the following:
Marked CRS \(M\in {\mathcal M}^ 0_ m\) is strict Markovian if and only if there is a subordinator in a random environment \((\nu_ t,\zeta_ t)\) on the same probability space for which \[ M_{(i)}=Clos\{\zeta_ t:\quad t\geq 0,\quad \nu_ t=i\},\quad i=1,...,m. \] Moreover the Laplace transformation of the Choquet capacity generated by strict Markovian marked CRS is obtained. Some examples connected with intersections for strict Markovian processes are given. In the theory of regenerative phenomena the corresponding object for strict Markovian marked CRS is a linked system of regenerative events.