A dual-range pressure switch apparatus has a piston member disposed in a switch mechanism containing chamber sealingly pertitioned by a diaphragm in the inner space of a housing, and being movable in the axial direction of chamber. A high-pressure snap disk is placed on the side surface of piston and contacts the diaphragm. In the chamber, a low-pressure snap disk is so arranged that its outer rim engages with the inner periphery of chamber and sandwich the piston between its center and the diaghragm. When the pressure of a pressurized fluid introduced in the inner space is lower than the lower limit of a certain range of values, both low and high snap disks are stable, so that paired resilient switch pieces disposed adjacent to the low snap disk in the chamber separate from each other. When the pressure is set in the certain range, only the low snap disk is transformed to push one switch piece to make it contact the other. When the pressure becomes higher than the upper limit of certain range, the high snap disk is then transformed to push a rod inserted through the piston and the low snap disk, so that the other switch piece is separated from the former transformed one switch piece.