A method of monitoring the thermomechanical behavior of an undersea pipe for transporting fluid under pressure, the undersea pipe being made by assembling together a plurality of unit pipe elements arranged end to end, the method comprising: • a step of determining a mechanical signature specific to each unit pipe element, which step consists in using at least one measurement cable having at least one optical fiber sensor using at least Brillouin backscattering and positioned along the entire length of the unit pipe element to measure the deformations experienced by or simulated on said unit pipe element while it is being subjected on land to various different mechanical stresses in predetermined directions and of predetermined magnitudes, and, on the basis of the deformation measurements, in establishing a stiffness matrix associated with the mechanical signature of the unit pipe element; • a step of determining a thermal signature specific to each unit pipe element, which step consists in using at least one measurement cable provided with at least one optical fiber sensor using at least Raman backscattering and positioned along the entire length of the unit pipe element to measure temperature changes of said unit pipe element while it is being subjected on land to various different electrical heating powers, and, on the basis of these temperature measurements, in establishing a thermal transfer function associated with the thermal signature of the unit pipe element; and • a monitoring step consisting in recovering the variations in the optical signal injected into the optical fiber sensors while the pipe is in service, and on the basis of these variations in the optical signal, in determining any changes in the mechanical and thermal signatures of each unit pipe element. • a step of determining a mechanical signature specific to each unit pipe element, which step consists in using at least one measurement cable having at least one optical fiber sensor using at least Brillouin backscattering and positioned along the entire length of the unit pipe element to measure the deformations experienced by or simulated on said unit pipe element while it is being subjected on land to various different mechanical stresses in predetermined directions and of predetermined magnitudes, and, on the basis of the deformation measurements, in establishing a stiffness matrix associated with the mechanical signature of the unit pipe element; • a step of determining a thermal signature specific to each unit pipe element, which step consists in using at least one measurement cable provided with at least one optical fiber sensor using at least Raman backscattering and positioned along the entire length of the unit pipe element to measure temperature changes of said unit pipe element while it is being subjected on land to various different electrical heating powers, and, on the basis of these temperature measurements, in establishing a thermal transfer function associated with the thermal signature of the unit pipe element; and • a monitoring step consisting in recovering the variations in the optical signal injected into the optical fiber sensors while the pipe is in service, and on the basis of these variations in the optical signal, in determining any changes in the mechanical and thermal signatures of each unit pipe element. <EOS>