We study in this paper dynamic equilibrium advertising strategies in a duopoly with asymmetric information structure. The advertising model of Lanchester is used in a game where the relevant solution concept is Feedback Stackelberg equilibrium which has the desirable property of being subgame perfect. An algorithm is devised for the computation of this equilibrium and numerical results are reported and discussed. Using a data set from the cola market, we analyze feedback advertising strategies and provide a comparison with closed-loop and open-loop Nash equilibria.