Whenever one deals with an interactive decision situation of long duration, one has to take into account that priorities of the participants may change during the conflict. In this paper we propose an extensive-form game model to handle such situations and suggest and study a solution concept, called credible equilibrium, which generalizes the concept of Nash equilibrium. We also discuss possible variants to this concept and applications of the model to other types of games. American Mathematical Society Classification Numbers: 90A06, 90A07, 90A43, 90A56, 90D06, 90D10, 90D35, 90D40, 90D80. Journal of Economic Literature Classification Numbers: C70, C72, D10, D11, D80, D83.