Since CO2 capture and storage (CCS) is a viable CO2 abatement option, CO2 capture power plants (CCPPs) could become a significant part of the future generation mix. This paper investigates the flexibility of the operation of a representative post-combustion CCPP with ancillary facilities. A mathematical model of the operation of such a plant is developed. This model quantifies the relation between the major operating characteristics of a CCPP, including efficiency penalty, capacity penalty, net power output, and net CO2 emission. On this basis, a profit maximization model is proposed. This model would help a CCPP decide its power output schedule, CO2 capture schedule, and bidding strategies in response of volatile power and carbon prices in a day-ahead energy market and a cap-and-trade carbon emission market. The validity and the usefulness of the proposed model are demonstrated using numerical results.