In the present paper multi-stage decision processes are considered in the case of complete as well as in the case of incomplete information on time-dependent influence quantities. It is shown, how to formulate the optimization problem in the case of incomplete information and how to solve it by means of functional equations. The results represent straighforward and natural generalizations of the functional equations for the case of complete information, which are known in the main. In both cases the parametrical way in considering the problem is crucial for application in technics, technology and economics.