This thesis examines the efficiency of the Australian foreign exchange and forward market between the first of January, 1986 and the first of August, 1991 for four currency relationships. Market efficiency is investigated with respect to purchasing power parity, covered interest rate parity, Fishers theorem and the unbiased forward rate hypotheses. Results, while in general consistent with the above parity conditions, indicate that significant deviations from such conditions existed within the Australian market during the period examined. However this thesis adopts the view that such results need not be inconsistent with market efficiency. Also, consistent with recent literature in the field, this study argues that included in returns in the foreign exchange market is a risk premium. Engle's test for an ARCH process is employed, where the existence of an ARCH process may be consistent with the existence of a risk premium. However while significant results are obtained from tests of the ARCH process, the conclusions drawn from this are limited.