In this Study, we used differential game theory to analyze the advertising and pricing strategies in a dual channel supply chain. The supply chain consisting of a manufacturer-retailer-consumer or traditional channel and a producer-consumer or online channel. Since the structure of the channel leading to the emergence of competition in the chain between manufacturer and retailer, to determine the equilibrium strategies of advertising volume and the price in both channels, the Nash equilibrium of the game was obtained. Study of this models of games by taking the time to be closer to the actual situation, we will emphasis on the use of differential models. Due to the dynamic strategies of the Nash equilibrium of the game and the continuity of the paths leading to equilibrium over time for each of these strategie. The feature of optimal path is that manufacturer and retailer at any given moment of time trying to make the best response to the strategy of the opponent. This process continues at the start of the game until end of the game led to a steady state equilibrium pathes for strategies. In this thesis, control variables are global advertising of manufacturer, online advertising of manufacturer, local advertising of retailer, the retailer's price and the manufacturer`s online price. These variables are not directly related to the function of the state variable of dynamic system. The state variable dynamical system is manufacturer`s goodwill. Such a dynamical system is called an autonomous dynamical system. After solving the problem and determine the paths of controls, state variable and profit functions of both online and retail channels, this results obtained: In the online channel, volume of online advertising is greater than the volume of retail advertising in traditional channel. The minimum size of the advertising is the manufacturer` global advertising. The equilibrium price in the online and traditional retail channels are greater than the manufacturer`s wholesale price. Equilibrium price of online channel and retailer`s channel are increasing over time, and the price in the online channel is always more than the price in traditional channel. Profit of manufacturer in online channel is always more than retailer`s profit in traditional channel. Sensitivity analysis of the equilibrium state variables, promotions, prices and profits from the sale of online and retail channels was performed. For increasing values of each parameter is given, and the other parameters held constant, the equilibrium level of the game to determine how these changes have examined. As a result, three of increase, decrease and mixed shifts of the equilibrium toward increasing values of model parameters was observed.