Motor vehicle battery wear monitoring system (1,1A,1B) including an acquisition device and a processing device/system (12,12A,12B); wherein the acquisition device is: • installable on board a motor vehicle that is equipped with an internal combustion engine, a battery for providing a battery voltage (V B), an alternator, and a starter motor for starting up the internal combustion engine; and • configured to receive the battery voltage (V B) and to output quantities indicative of said battery voltage (V B); and wherein the processing device/system (12,12A,12B) is: • configured to receive the quantities indicative of the battery voltage (V B) from the acquisition device; and • programmed to perform a battery voltage monitoring based on the quantities indicative of the battery voltage (V B) to detect an approaching battery failure; wherein the battery voltage monitoring includes detecting for each start-up of the internal combustion engine: • a respective first voltage value (V MIN) that is a minimum value assumed by the battery voltage (V B) just after the starter motor has started operating to start up the internal combustion engine; and • a respective second voltage value (V 2) assumed by the battery voltage (V B) just after the internal combustion engine has been started up, the starter motor has stopped operating and the alternator has started operating; characterized in that the battery voltage monitoring further includes for each start-up of the internal combustion engine: • computing a respective voltage rise value (ΔV R) indicative of a difference between the respective first (V MIN) and second (V 2) voltage values; and • detecting an approaching battery failure if the respective voltage rise value (ΔV R) meets a predefined condition with respect to a predefined voltage rise threshold (T ΔVR). • installable on board a motor vehicle that is equipped with an internal combustion engine, a battery for providing a battery voltage (V B), an alternator, and a starter motor for starting up the internal combustion engine; and • configured to receive the battery voltage (V B) and to output quantities indicative of said battery voltage (V B); and wherein the processing device/system (12,12A,12B) is: • configured to receive the quantities indicative of the battery voltage (V B) from the acquisition device; and • programmed to perform a battery voltage monitoring based on the quantities indicative of the battery voltage (V B) to detect an approaching battery failure; • configured to receive the quantities indicative of the battery voltage (V B) from the acquisition device; and • programmed to perform a battery voltage monitoring based on the quantities indicative of the battery voltage (V B) to detect an approaching battery failure; wherein the battery voltage monitoring includes detecting for each start-up of the internal combustion engine: • a respective first voltage value (V MIN) that is a minimum value assumed by the battery voltage (V B) just after the starter motor has started operating to start up the internal combustion engine; and • a respective second voltage value (V 2) assumed by the battery voltage (V B) just after the internal combustion engine has been started up, the starter motor has stopped operating and the alternator has started operating; • a respective first voltage value (V MIN) that is a minimum value assumed by the battery voltage (V B) just after the starter motor has started operating to start up the internal combustion engine; and • a respective second voltage value (V 2) assumed by the battery voltage (V B) just after the internal combustion engine has been started up, the starter motor has stopped operating and the alternator has started operating; characterized in that the battery voltage monitoring further includes for each start-up of the internal combustion engine: • computing a respective voltage rise value (ΔV R) indicative of a difference between the respective first (V MIN) and second (V 2) voltage values; and • detecting an approaching battery failure if the respective voltage rise value (ΔV R) meets a predefined condition with respect to a predefined voltage rise threshold (T ΔVR). • computing a respective voltage rise value (ΔV R) indicative of a difference between the respective first (V MIN) and second (V 2) voltage values; and • detecting an approaching battery failure if the respective voltage rise value (ΔV R) meets a predefined condition with respect to a predefined voltage rise threshold (T ΔVR).