The objective of the thesis is to construct bioeconomic models describing the two stocks of Patagonian toothfish residing in the Macquarie Island Fishery. A bioeconomic model combines the economic production function and the biological production function relevant to the fishery. The biological production function can be described in two ways, one as the discrete biomass model, describing the stock as a single parameter. The second is as the continuous cohort model, describing the stock in its different age-classes. Each of these production functions are described in detail in Chapters 3 to 6. The two bioeconomic models will provide similar results for the economically efficient levels of stock and harvest. The bioeconomic models will be used to predict open-access levels of stock and economically efficient stock levels that maximise the net present value of the fishery. The results are used to formulate harvesting strategies for 'Country A' that will continue to maximise net revenue when a second country begins to illegally fish the same stock. It is hoped that the results obtained from this paper will contribute to management and policy decisions regarding the Patagonian toothfish fishery.