This paper is devoted to the Travelling Salesman Problem as applied to Czechoslovak ocean shipping companies and their marine ports on the Black Sea. The shortest circular path around these ports is found and discussed. Formulation of the problem accounts for the fact that distances between the individual cities are not the same in both directions. The consequences that arise from this situation are studied. The used algorithms are based on graph theory and standard logistic methods. In addition, the results are compared with the results obtained by using a minimum spanning tree algorithm.