This note examines the weak-form market efficiency of the Australian stock market. Daily returns from 6 January 1958 to 12 April 2006 and monthly returns from February 1875 to December 2005 are examined for random walks using serial correlation coefficient and runs tests, Augmented Dickey-Fuller, Phillips-Perron and Kwiatkowski, Phillips, Schmidt and Shin unit root tests and multiple variance ratio tests. The serial correlation tests indicate inefficiency in daily returns and borderline efficiency in monthly returns, while the runs tests conclude that both series are weak-form inefficient. The unit root tests suggest weak-form inefficiency in both return series. The results of the more stringent and least restrictive variance ratio tests indicate that the monthly returns series is characterised by a homoskedastic random walk, but the daily series violates weak-form efficiency because of the short-term autocorrelation in returns.