This paper deals with the simultaneous optimization of the operating conditions and sizes of each one of the process units of a natural gas combined cycle coupled to a postcombustion CO2 capture system. Precisely, from the mathematical models previously developed by the authors for each stand-alone process, a new optimization nonlinear programming (NLP) model is proposed in order to optimize the whole process but with the main characteristic that several feasible alternatives to integrate both processes are simultaneously embedded. Therefore, as a result of the model, the best integration schema, optimal operating conditions, and size of each process unit are obtained at the same time. No integer variables are needed to model discrete decisions in both processes. The maximization of the overall thermal efficiency is considered as an objective function. However, the proposed NLP model can be easily extended into a mixed-integer nonlinear programming (MINLP) model if it is necessary for cost minimization. The optimization results are discussed in detail, and they are compared with suboptimal configurations including reference cases.