Process for checking that complete threads are engaged when tightening an assembly comprising at least a first part and a second part and a threaded fastener, comprising a first component and a second component, the process comprising at least the following stages: - a stage of measuring at least one torque from a coupling torque and a reaction torque in the threaded fastener while keeping one of the components of the threaded fastener fixed, - a stage of measuring another parameter, other than torque, preferably a time, an axial displacement or again an angle of rotation between the first and second parts, - a stage of determining a function representing a change in torque in relation to the other parameter for torque values between 0 and the final torque value, - a stage of analysing the function comprising: • a stage of identifying the portions of the function, the said portions together making up the function, and their corresponding gradient values, • a stage of comparing the gradient value for each portion of the function with each of the previously determined gradient values of a first theoretical and/or experimental reference function which is characteristic of correct defect-free assembly and with each of the predetermined gradient values of a second theoretical and/or experimental reference function which is characteristic of incorrect assembly with tightening on incorrectly formed threads, and - a checking stage comprising: • checking that the value of the gradient of a portion of the function is zero, this portion of the function forming a non-zero plateau in relation to values of the other parameter, • checking that the value of the gradient of a last portion of the function defined after the portion forming the plateau for torques which are equal to at least the torque of the portion forming the plateau is equal to a gradient value characteristic of correct assembly, • checking that none of the values for the gradients of the portions of function defined after a portion forming the plateau is equal to a gradient value of the second reference function corresponding to tightening on incorrectly formed threads, and if at least one of the checks in the checking stage is not satisfactory the process comprises a stage informing that tightening has not been carried out correctly. - a stage of measuring at least one torque from a coupling torque and a reaction torque in the threaded fastener while keeping one of the components of the threaded fastener fixed, - a stage of measuring another parameter, other than torque, preferably a time, an axial displacement or again an angle of rotation between the first and second parts, - a stage of determining a function representing a change in torque in relation to the other parameter for torque values between 0 and the final torque value, - a stage of analysing the function comprising: • a stage of identifying the portions of the function, the said portions together making up the function, and their corresponding gradient values, • a stage of comparing the gradient value for each portion of the function with each of the previously determined gradient values of a first theoretical and/or experimental reference function which is characteristic of correct defect-free assembly and with each of the predetermined gradient values of a second theoretical and/or experimental reference function which is characteristic of incorrect assembly with tightening on incorrectly formed threads, and • a stage of identifying the portions of the function, the said portions together making up the function, and their corresponding gradient values, • a stage of comparing the gradient value for each portion of the function with each of the previously determined gradient values of a first theoretical and/or experimental reference function which is characteristic of correct defect-free assembly and with each of the predetermined gradient values of a second theoretical and/or experimental reference function which is characteristic of incorrect assembly with tightening on incorrectly formed threads, and - a checking stage comprising: • checking that the value of the gradient of a portion of the function is zero, this portion of the function forming a non-zero plateau in relation to values of the other parameter, • checking that the value of the gradient of a last portion of the function defined after the portion forming the plateau for torques which are equal to at least the torque of the portion forming the plateau is equal to a gradient value characteristic of correct assembly, • checking that none of the values for the gradients of the portions of function defined after a portion forming the plateau is equal to a gradient value of the second reference function corresponding to tightening on incorrectly formed threads, and • checking that the value of the gradient of a portion of the function is zero, this portion of the function forming a non-zero plateau in relation to values of the other parameter, • checking that the value of the gradient of a last portion of the function defined after the portion forming the plateau for torques which are equal to at least the torque of the portion forming the plateau is equal to a gradient value characteristic of correct assembly, • checking that none of the values for the gradients of the portions of function defined after a portion forming the plateau is equal to a gradient value of the second reference function corresponding to tightening on incorrectly formed threads, and