Tuberculosis (TB) was thought to be safely in decline in the United States in the mid 1980's as the number of cases dropped by 74% between 1953 and 1985. A wake-up call was issued in 1986 as an increase in TB incidence which could not be accounted for was reported. This upward trend has continued. At of the end of 1992, the CDC estimated that 39,000 more cases of TB had developed over the previous decade than if the declining trend present in the early 1980's had continued. This turnaround in TB is well correlated with the rise of the HIV epidemic. The severely depressed immune systems associated with HIV make individuals infected with the virus more likely to develop active TB than those who are not infected. Whereas susceptibles to HIV are generally confined to high risk groups such as homosexuals or intravenous drug users, this is not the case with TB. It may be that the development of the HIV epidemic has somehow tipped the balance in favor of a continued rise in TB within the United States. The purpose of this work is to investigate through the use of mathematical models the magnitude and duration of the effect which the HIV epidemic may have on TB. Deterministic and stochastic models are developed which reflect the transmission dynamics of both TB and HIV, and the relative merits of these models are discussed. The deterministic models are then linked together to form a model for the combined spread of both diseases. A numerical study is performed to investigate the influence of certain key parameters. The effect which HIV will have on the general population is found to be dependent on the contact structure between the general population and the HIV risk groups as well as a possible shift in the dynamics associated with TB transmission. The development of a TB epidemic within the HIV risk groups is also considered.