Compressor rapid cycling has been shown to be capable of delivering the advantages of variable capacity control without the use of variable speed compressors. For automotive air conditioning systems, rapid cycling can be achieved by engaging and disengaging the clutch drive. However, rapid cycling results in oscillations in evaporator superheat which degrade system performance and may damage the compressor. This paper discusses the dynamics associated with compressor rapid cycling and possible system configurations and control strategies for modulating the expansion valve to regulate superheat during rapid cycling operation. These strategies include feedback control strategies such as thermostatic expansion valve (TXV), and PI control, as well as feedforward control strategies. The feedback control strategies regulate the average superheat temperature, but fail to eliminate the oscillations caused by rapid cycling. The addition of feedforward control is shown to eliminate the superheat oscillations in simulation. However, basic physical limitations of the valve and overall system prevent the complete elimination of these undesirable dynamics in practice.