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The paper addresses the existence of an equilibrium unemployment-vacancies (UV) relationship in Australia. Cointegration test results suggest that no bivariate long-run (UV) relationship exists. Moreover, this finding fails to support the basic model of labour job search. However, a modified Beveridge Curve is proposed where it is found that a number of trivariate equilibrium relationships exist between unemployment, vacancies and one other variable; the replacement ratio, the proportion of long-term unemployed or the real wage. The existence of an equilibrium relationship in the multivariate framework is due to the endogenous modelling of the (un)employment flows which are assumed to be exogenous in the bivariate framework of the Beveridge Curve.