Abstract. In this paper we will investigate the semi-markov random processes with positive tendency, negative jumps and delaying boundary at zero in this article.The
Laplace transform on time,Laplace-Stieltjes transform on phase of the conditional and unconditional distributions and Laplace-Stieltjes transform of the ergodic distribution
are defined. The characteristics of the ergodic distribution will be calculated on the basis of the final results.