The trend toward the energy efficiency improvement for transcritical carbon dioxide refrigeration cycles has led to the development of the two-stage compression process. Three different variations of transcritical carbon dioxide two-stage compression cycles with expanders are investigated by using thermodynamics analysis. They are the two-stage compression at optimal intermediate pressure (TCOP) cycle, two-stage compression with expander driving high-pressure stage (TCDH) cycle and two-stage compression with expander driving low-pressure stage (TCDL) cycle, respectively. The performance of the TCOP cycle and the single-stage compression with expander (SCE) cycle is mainly discussed and compared for a wide operating condition. It is found that the COP and exergy efficiency of the TCOP cycle are on average 9% higher than those of the SCE cycle. At given design points, the COP of the TCDH cycle outperforms the other options, showing 11.32%, 9.65% and 0.72% performance improvement over the TCDL cycle, SCE cycle and the TCOP cycle, respectively. If design and structure are also taken into account, the TCDH cycle is a feasible option since the expander and the auxiliary compressor are integrated into one unit; thus, the transfer loss and leakage loss can be decreased greatly. The key problem is to adopt some measures that control the operating conditions to avoid deviating from the design point. (c) 2006 Elsevier Ltd. All rights reserved.