Due to their high propulsive efficiency, counter-rotating open rotors (CRORs) have the potential to significantly reduce fuel consumption and emissions relative to conventional high bypass ratio turbofans. However, this novel engine architecture presents many design and operational challenges both at engine and aircraft level. The assessment of the impact of the main low-pressure preliminary design and control parameters of CRORs on mission fuel burn, certification noise, and emissions is necessary at preliminary design stages in order to identify optimum design regions. These assessments may also aid the development process when compromises need to be performed as a consequence of design, operational, or regulatory constraints. The required preliminary design simulation tools should ideally be 0D or 1D (for computational purposes) and should capture the impact of the independent variation of the main low-pressure system design and control variables, such as the number of blades, diameter and rotational speed of each propeller, the spacing between the propellers, and the torque ratio (TR) of the gearbox or the counter-rotating turbine (CRT), among others. From a performance point of view, counter-rotating propellers (CRPs) have historically been modeled as single propellers. Such a performance model does not provide the required flexibility for a detailed design and control study. Part I of this two-part publication presents a novel 0D performance model for CRPs allowing an independent definition of the design and operation of each of the propellers. It is based on the classical low-speed performance model for individual propellers, the interactions between them, and a compressibility correction which is applied to both propellers. The proposed model was verified with publicly available wind tunnel test data from NASA and was judged to be suitable for preliminary design studies of geared and direct drive open rotors. The model has to be further verified with high-speed wind tunnel test data of highly loaded propellers, which was not found in the public domain. In Part II, the novel CRP model is used to produce a performance model of a geared open rotor (GOR) engine with a 10% clipped propeller designed for a 160 PAX and 5700 NM aircraft. This engine model is first used to study the impact of the control of the propellers on the engine specific fuel consumption (SFC). Subsequently, it was integrated in a multidisciplinary simulation platform to study the impact of the control of the propellers on engine weight, certification noise, and NOx emission.