Two clocks, a fast clock and a slow clock are provided for clocking a processing unit. A plurality of frequency settings, referred to as gears, are defined for the two clock. Each of these gears indicates a maximum frequency for the fast clock and a minimum frequency for the slow clock, such that the gap between the two frequencies may be kept to a manageable level so as to reduce transients upon switching between the two clocks. The system switches between the gears as required. In response to a determination to increase the frequency of the clock signal, a higher gear is selected at which the maximum and minimum frequencies defined for that gear are higher than the previous selected gear.