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This paper proposes an empirical methodology for studying various (implicit or explicit) collusive behaviors on two strategic variables, which are price and advertising, in a differentiated market dominated by a duopoly. In addition to Nash or Stackelberg behaviors, we consider collusion on both variables, collusion on one variable and competition on the other, etc. Using data on the Coca-Cola and Pepsi-Cola markets from 1968 to 1986, full information maximum likelihood estimation of cost and demand functions are obtained allowing for various collusive behaviors. The collusive hypothesis is not rejected, and the best form of collusive behavior is selected via nonnested testing procedures. Using the best model, Lerner indices are computed for both duopolists to provide summary measures of market power. Finally, our approach is contrasted with the conjectural variation approach and is shown to give superior results.