With a certain pipeline, either underground or deposited on a sea/lake bottom, the formation of critical faults is determined and localized, which arise in the walls of the pipeline, or the growth of an already localized fault is monitored, through a method which detects, by acoustic sensors regularly distributed along the pipeline, the ultrasounds diffused along the walls of the pipeline itself upon the formation of a critical fault, or when a controlled fault increases, and processing, by a remote processor, the digital signals associated with the sound waves to identify the position or evaluate the development of a critical fault.