The circular shift register is a versatile building block for RSFQ digital circuits. It can be used for local memory and it is essential for the proposed implementation of residue number system arithmetic. It is surprising that the successful recurrent operation of such a shift register has never been reported m the RSFQ literature. Circular shift registers have a design constraint that is unusual in RSFQ circuits-the requirement of zero overall clock skew. We propose and analyze three novel designs and compare their simulated parameter margins as well as their maximum operating frequencies, latencies and areas. These designs differ in the topology of the clock distribution network as well as the type of storage element employed in the data path. Two designs show satisfactory parameter margins and large maximum clock frequency.