Method of acoustic monitoring for the detection of leaks in an underwater structure containing a fluid under pressure, said monitoring method comprising the following steps: - acquiring an acoustic signal in an area surrounding said underwater structure by means of at least one underwater acoustic sensor; - carrying out a pre-processing of said acoustic signal so as to obtain an acoustic synthesis signal by means of at least one underwater processing unit; - transmitting said acoustic synthesis signal to an external processing unit arranged at the surface in a floating position; - carrying out a processing of said acoustic synthesis signal by means of said external processing unit so as to determine at least one variable parameter over time representative of the intensity of the spectral components of said acoustic synthesis signal; - comparing the value of said at least one parameter representative of the intensity, with the value of a corresponding threshold parameter that is variable in the predetermined time, said threshold parameters being determined based upon historical data; - generating an alarm signal when the value of said at least one parameter representative of the intensity exceeds the value of said corresponding threshold parameter, said alarm signal indicating the presence of a leak wherein said step of acquiring said acoustic signal is carried out by means of an omni-directional acoustic sensor and said pre-processing step comprises the following steps: - amplifying said acquired acoustic signal and filtering said amplified signal in a first predetermined frequency band; - translating said amplified and filtered signal in a second predetermined frequency band; - determining said acoustic synthesis signal by calculating the logarithm of the power spectrum of said signal translated in frequency and then calculating its weighted average value in a certain number of frequency bands. - acquiring an acoustic signal in an area surrounding said underwater structure by means of at least one underwater acoustic sensor; - carrying out a pre-processing of said acoustic signal so as to obtain an acoustic synthesis signal by means of at least one underwater processing unit; - transmitting said acoustic synthesis signal to an external processing unit arranged at the surface in a floating position; - carrying out a processing of said acoustic synthesis signal by means of said external processing unit so as to determine at least one variable parameter over time representative of the intensity of the spectral components of said acoustic synthesis signal; - comparing the value of said at least one parameter representative of the intensity, with the value of a corresponding threshold parameter that is variable in the predetermined time, said threshold parameters being determined based upon historical data; - generating an alarm signal when the value of said at least one parameter representative of the intensity exceeds the value of said corresponding threshold parameter, said alarm signal indicating the presence of a leak wherein said step of acquiring said acoustic signal is carried out by means of an omni-directional acoustic sensor and said pre-processing step comprises the following steps: - amplifying said acquired acoustic signal and filtering said amplified signal in a first predetermined frequency band; - translating said amplified and filtered signal in a second predetermined frequency band; - determining said acoustic synthesis signal by calculating the logarithm of the power spectrum of said signal translated in frequency and then calculating its weighted average value in a certain number of frequency bands. - amplifying said acquired acoustic signal and filtering said amplified signal in a first predetermined frequency band; - translating said amplified and filtered signal in a second predetermined frequency band; - determining said acoustic synthesis signal by calculating the logarithm of the power spectrum of said signal translated in frequency and then calculating its weighted average value in a certain number of frequency bands.