Binary-flashing units utilize new types of geothermal power cycles, which may be used with resources of relatively low temperatures (less than 150°C) where other cycles result in very low efficiencies. The thermodynamic cycles for the binary flashing units are combinations of the geothermal binary and flashing cycles. They have most of the advantages of these two conventionally used cycles, but avoid the high irreversibilities associated with some of their processes. Any fluid with suitable thermodynamic properties may be used in the secondary Rankine cycle. At the optimum design conditions binary-flashing geothermal power plants may provide up to 25 percent more power than the conventional geothermal units.