Most models of the spread of HIV/AIDS assume that the probability of transmission from an infected individual to a susceptible partner has some constant value per sexual act, compounding independently randomly (so that ten acts with one person chosen from a particular group has, on average, the same risk as one act with each of ten different people from that group). Guided by available data, other models treat the transmission process as being some characteristic (but highly variable) value per partnership, independent of the number of acts. This latter approach does not allow for the possible effects of concurrent partnerships, and therefore does not take account of the possibility that an initially uninfected partner of a given susceptible individual may become infected over the duration of their partnership. We present a new model, based on transmission per partnership, that takes account of partnership duration. If the number of overlapping partnerships is high enough (so that R0 greater than 1 among "standing crops" of partners), any initial infection will spread very fast--on the time scale of a few times the latent interval (a few months)--among existing networks of partners. After this initial "fast phase," the subsequent epidemic proceeds more slowly along conventional lines as new partnerships are formed. These properties of the model are illustrated numerically and by analytic studies (using singular perturbation theory). The possibility of such "two time-scale" phenomena could have implications for data analysis based on statistical back-projection.