For waste-heat recovery applications, operating an organic Rankine cycle (ORC) with two-phase expansion has been shown to increase the utilisation of the waste-heat stream, leading to a higher power output compared to a conventional ORC with single-phase expansion. However, unlike the conventional ORC, working-fluid selection for an ORC operating with two-phase expansion has not been explored in detail within the literature. Therefore, the aim of this paper is to explore which working-fluid parameters make a particular working fluid suitable for this type of cycle. This is conducted by coupling a thermodynamic model of the cycle with the Peng-Robinson cubic equation of state. Moreover, the effect of the expander volumetric ratio on the expander isentropic efficiency is accounted for using a performance model for a twin-screw expander. Ultimately, the adopted approach allows the effect of the working-fluid parameters, namely the critical temperature and ideal specific-heat capacity, on both the expander performance and the cycle to be evaluated in a generalised way. For the investigation, 15 theoretical working fluids are defined, covering five different critical temperatures, with a negatively-sloped, vertical and positively-sloped saturated vapour line respectively. The 15 working fluids are selected as they represent the feasible design space occupied by existing ORC working fluids. For each fluid, a cycle optimisation is completed for different heat-source temperatures ranging between 80 and 200 Β°C. The objective is to identify the optimal cycle operating conditions that result in maximum power output from the system. By analysing the results, the optimal characteristics of a working fluid are obtained, and this information can be used to identify physical working fluids which are good candidates for a particular heat-source temperature. In the final part of this paper, the cycle optimisation is repeated for the physical working fluids identified, thus validating the suitability of the approach developed. Ultimately, the results can help to narrow down the search space when considering working fluids for an ORC operating with two-phase expansion