The paper considers the continuous-time Markov branching system. We are interested in a case when an average intensity of the branching rate \(m\ne {0}\) is called the noncritical case. It was proved by Sevastyanov [25] that the average expected number of population sizes on the survival trajectories of subcritical system, \(m<0\) , asymptotically stabilizes and approaches , where is an analogue of the Kolmogorov constant, which we call the same. The principal aim of this paper is to find an explicit expression for this constant. We will calculate it as a function of infinitesimal factorial moments of the system branching rate. First, we will establish an asymptotic expansion of the generating function of the probability of the number of individuals as the Basic Lemma of the noncritical Markov branching systems theory. Our further discussion is essentially based on this lemma. This lemma immediately gives us the "noncritical analogue" of constant . As a consequence, we refine several limit results of the theory of noncritical Markov branching systems by specifying explicit leading terms in the asymptotic expansions.
