It is well known that the CAPM beta is not stable over time. We investigate the nature of the time-variation in betas using monthly Australian data from 1979 to 1994 for 23 sectors. We discuss beta estimates for sub-periods and tests of the statistical adequacy of the market model used to estimate the betas. We estimate time-varying betas using recursive regressions, rolling regressions and using the Kalman Filter. We find considerable time-variation in the estimated betas and find that many are non-stationary. We estimate a simple model which explains the variation in each of the betas in terms of a time trend, allowing for a break both in level and in trend at October 1987. The model explains a large proportion of the variation in the betas over the sample period for most of the sectors. (C) 1999 IMACS/Elsevier Science B.V. All rights reserved.