Many writers have discovered the existence of asymmetric adjustment in labour market variables for several GECD countries. This thesis examines whether this is the case for particular Australian labour market variables and relationships including total employment, the unemployment rate, the Beveridge Curve (unemployment and vacancies), and real wages. These variables / relationships are tested for omitted nonlinearities using a BDS test. Given that significant non-linear adjustment appears to exist in these variables, attempts are then made to model economically interesting forms of nonlinearity and asymmetry. In particular, the relationship with the state of the business cycle is examined. It is investigated as to whether the non-linearities in the labour market are captured well using a non-linear measure of the business cycle as derived from a two-state Markovian regime-switching model. This appears to be successful for some aspects of labour market behaviour. The thesis also examines the dynamic labour market equilibrium relationship between real wages, unemployment rate and labour productivity. Dynamic asymmetries in the operation of the labour market are estimated using a Threshold Autoregressive (TAR) process, and an error correction model (ECM) is estimated for the adjustment dynamics in order to return the labour market to equilibrium. The extended 'stylised facts' documented in this thesis provide important insight into the underlying structure of the Australian labour market. They have important implications for economic modeling of labour markets and the macroeconomy in general. Extending our understanding in such ways leads. to potentially important implications for economic policy. Several policy-related suggestions are made in regards to finding economically interesting non-linearities and asymmetries in the Australian labour market.