Transonic flows through axial, multistage, transcritical organic rankine cycle (ORC) turbines are investigated by using a numerical solver including advanced multiparameter equations of state and a high-order discretization scheme. The working fluids in use are the refrigerants R134a and R245fa, classified as dense gases due to their complex molecules and relatively high molecular weight. Both inviscid and viscous numerical simulations are carried out to quantify the impact of dense gas effects and viscous effects on turbine performance. Both supercritical and subcritical inlet conditions are studied for the considered working fluids. In the former case, flow across the turbine is transcritical, since turbine output pressure is subcritical. Numerical results show that, due to dense gas effects characterizing the flow at supercritical inlet conditions, supercritical ORC turbines enable, for a given pressure ratio, a higher isentropic efficiency than subcritical turbines using the same working fluid. Moreover, for the selected operating conditions, R134a provides a better performance than R245fa.