With increasing concerns on global warming, reduction of $CO_2$ emission has become a hot issue and studies of $CO_2$ capture and storage (CCS) technology in power plant applications are in progress. Oxy-fuel combustion is one of the several available technologies that intend to capture $CO_2$, Since the combustion gas consists mainly of $CO_2$ and $H_2O$ in oxy-fuel combustion systems, it is easy to separate $CO_2$ from the flue gas using a simple mechanical method instead of complex chemical processes. There have been suggested a couple of power cycles using different recirculation fluids for combustion dilution purpose. This study aimed to investigate the influence of $CO_2$ capture on the performance of two promising oxy-fuel combustion power cycles adopting $H_2O$ and $CO_2$ as the recirculation fluid. Optimal integration between the carbon capture process and the power cycle was examined and the influences of carbon capture on the entire system performance were compared for the two cycles.