Theoretical models are presented for calculation of the bed turnover time in both the slumping and rolling modes and the slumping-to-rolling transition in rotating drums with less than 50% volumetric fill of free-flowing granular materials. It is suggested that the transition from slumping to rolling occurs when the two turnover times are equal. The model for the bed turnover time in rolling beds is compared with the data reported in the literature. Very good agreement has been obtained. The bed turnover time is also employed to define a new Froude number for constructing the bed behaviour diagram. It is shown that the bed behaviour diagram based on the new Froude number brings the data points for sand and limestone into single curves. The implications of the bed turnover time for solid mixing and heat transfer within particle beds are also discussed.