We use two coupled equations to analyze the space/time dynamics of two interacting languages. First, we introduce a cohabitation model, which is more appropriate for human populations than classical (noncohabitation) models. Second, using numerical simulations, we find the front speed of a new language spreading into a region in which another language was previously used. Third, for a special case, we derive an analytical formula that makes it possible to check the validity of our numerical simulations. Finally, as an example, we find that the observed front speed for the spread of the English language into Wales in the period 1961 through 1981 is consistent with the model predictions. We also find that the effects of linguistic parameters are much more important than the effects of parameters related to population dispersal and reproduction. If the initial population densities of both languages are similar, they have no effect on the front speed. We outline the potential of the new model to analyze relationships between language replacement and genetic replacement.