We apply a logistic smooth transition market model (LSTM) to a sample of returns on Australian industry portfolios to investigate whether bull and bear market betas differ. Unlike other studies, our LSTM model allows for smooth transition between bull and bear states and allows the data to determine the threshold value. The estimated value of the smoothness parameter was very large for all industries implying that transition is abrupt. Therefore we estimated the threshold as a parameter along with the two betas in a dual beta market (DBM) framework using a sequential conditional least squares (SCLS) method. Using Lagrange Multiplier type tests of linearity, and the SCLS method our results indicate that for all but two industries the bull and bear betas are significantly different.