Power management method for a detector of the position of a mobile fitting part carried by an edge (5; 6) belonging to a sash or a frame of a framework, such as a door, a window or a shutter, the fitting part being mobile along a path comprising several distinct ranges (C221, C222, C223) of positions of the fitting part relative to the edge (5; 6), the detector comprising: • a battery (30, 32); • sensor systems (99A, 99B; 99C; 99D, 99E), which are powered by the battery (30, 32), each sensor system (99A, 99B; 99C; 99D, 99E) being respectively associated with one of the ranges (C221, C222, C223) and being configured to adopt an operating mode, wherein said sensor system (99A, 99B; 99C; 99D, 99E) returns at least: ◆ an affected state, if the fitting part is positioned in the range (C221, C222, C223) associated with said sensor system (99A, 99B; 99C; 99D, 99E), and ◆ an unaffected state, if the fitting part is positioned outside the range (C221, C222, C223) associated with said sensor system (99A, 99B; 99C; 99D, 99E); • an electronic analyser, which is configured to determine position information of the fitting part along the path, based on the respective status returned by the sensor systems (99A, 99B; 99C; 99D, 99E); and • an electronic transmitter, for transmitting the position information determined by the electronic analyser; characterised in that the method comprises: • memorizing which sensor system (99A, 99B; 99C; 99D, 99E) is last in the affected state while the detector is in a wake-up mode; • while the detector is in wake-up mode, automatically switching the detector into a power-saving mode including: ◆ retaining in operating condition the sensor system (99A, 99B; 99C; 99D, 99E) that was memorized, and ◆ switching every other sensor system (99A, 99B; 99C; 99D, 99E) that was in the operating mode to a stand-by mode; and • automatically switching the detector to wake-up mode, when the sensor system (99A, 99B; 99C; 99D, 99E) that was memorized changes state while the detector is in power-saving mode, the automatic switch to wake-up mode including a switchover of at least one of the sensor systems (99A, 99B; 99C; 99D, 99E) that was in the stand-by mode to the operating mode. • a battery (30, 32); • sensor systems (99A, 99B; 99C; 99D, 99E), which are powered by the battery (30, 32), each sensor system (99A, 99B; 99C; 99D, 99E) being respectively associated with one of the ranges (C221, C222, C223) and being configured to adopt an operating mode, wherein said sensor system (99A, 99B; 99C; 99D, 99E) returns at least: ◆ an affected state, if the fitting part is positioned in the range (C221, C222, C223) associated with said sensor system (99A, 99B; 99C; 99D, 99E), and ◆ an unaffected state, if the fitting part is positioned outside the range (C221, C222, C223) associated with said sensor system (99A, 99B; 99C; 99D, 99E); ◆ an affected state, if the fitting part is positioned in the range (C221, C222, C223) associated with said sensor system (99A, 99B; 99C; 99D, 99E), and ◆ an unaffected state, if the fitting part is positioned outside the range (C221, C222, C223) associated with said sensor system (99A, 99B; 99C; 99D, 99E); • an electronic analyser, which is configured to determine position information of the fitting part along the path, based on the respective status returned by the sensor systems (99A, 99B; 99C; 99D, 99E); and • an electronic transmitter, for transmitting the position information determined by the electronic analyser; • memorizing which sensor system (99A, 99B; 99C; 99D, 99E) is last in the affected state while the detector is in a wake-up mode; • while the detector is in wake-up mode, automatically switching the detector into a power-saving mode including: ◆ retaining in operating condition the sensor system (99A, 99B; 99C; 99D, 99E) that was memorized, and ◆ switching every other sensor system (99A, 99B; 99C; 99D, 99E) that was in the operating mode to a stand-by mode; and ◆ retaining in operating condition the sensor system (99A, 99B; 99C; 99D, 99E) that was memorized, and ◆ switching every other sensor system (99A, 99B; 99C; 99D, 99E) that was in the operating mode to a stand-by mode; and • automatically switching the detector to wake-up mode, when the sensor system (99A, 99B; 99C; 99D, 99E) that was memorized changes state while the detector is in power-saving mode, the automatic switch to wake-up mode including a switchover of at least one of the sensor systems (99A, 99B; 99C; 99D, 99E) that was in the stand-by mode to the operating mode.