Bilateral exchange rates are widely discussed in the public arena. Most developed economies have, in the last three decades, consciously moved from a fixed exchange rate regime to something approximating a purely floating regime. In conjunction with this change has been the increased attention that the concept of an exchange rate equilibrium has received from many academic economists, including those in many central banks. Large fluctuations in exchange rates over the period have, however, left many observers to wonder whether such movements have been consistent with equilibrium behaviour or whether the currencies have been, in some sense, misaligned. This issue is further complicated by the fact that there is no single accepted definition or measure of exchange rate equilibrium, but rather the choice of model depends on the question at hand. The Australian exchange rate, in particular, has undergone a number of deep fluctuations in recent years. Consequently, a number of questions have arisen with respect to what the drivers of such fluctuations have been and whether there has been an element of misalignment to these factors. Currently, there has been little academic work regarding the measurement of an Australian equilibrium exchange rate. By surveying the literature on behavioural equilibrium exchange rates (BEERs) as well as a number of other equilibrium measures, this dissertation seeks to address this gap by constructing a CHEER (a nominal exchange rate version of a BEER) model for the Australia-US bilateral exchange rate. The results of this analysis suggest that the exchange rate has been misaligned for substantial periods since floating, on average around 12 percent. The suggestion is that at December 2006, the end of the data sample considered, the exchange rate was 15 percent over-valued, which is consistent with PPP based estimates, similar to measurements reported by the Pacific Exchange Rate Service. To further analyse the importance of substantial exchange rate fluctuations, an examination of the links between productivity and the exchange rate in an Australian context is also provided. It is found, consistent with a number of the other studies, that the traditional links between the exchange rate and productivity are muddied by a number of short term forces. Australia has significantly lagged behind a number of its nearest trading neighbours in terms of productivity growth for extended periods over the last three decades, which according to the Balassa-Samuelson hypothesis would have led to a depreciation of the real exchange rate. In fact the opposite is true; the Australian-US bilateral real exchange rate has appreciated strongly in recent times. Causes of this appreciation have included the dramatic terms of trade increases that have been observed as well as sustained effects of speculative forces through the so-called carry trade. The world wide commodity price boom, which has fuelled significant export growth of minerals from Australia to the rest of the world, is argued to be the main factor underlying these dramatic increases.