The paper desribes the application of elements of the game theory for the purpose of optimal of some dynamic continuous processes. Using as an example the process of safe ship’s, the paper presents the problem of applying a positional non-cooperative game and multi-step matrix game of j objects for the description of the process considered as well as for the synthesis of optimal strategies. A mathematical model of dynamic game is formulated and its approximation in the form of dual linear programming problem is used for the synthesis of safe ship’s trajectory as a multistage process decision. The considerations have been illustrated an example of a computer simulation the POSGAME and RISKGAME algorithms to determine the safe ship’s trajectory in situation of passing a big number of the objects encountered, recorded on the radar screen in real navigational situation at sea.