A method of making safe the operation of a rotary assembly of a turbomachine, which rotary assembly comprises both a turbine that is caused to rotate by expansion of a drive fluid that is to flow through the turbine, and a rotary machine that is driven mechanically in rotation by the turbine so as to move a driven fluid that is to flow through the rotary machine, the method being characterized in that the event of the rotary assembly exceeding a predetermined threshold speed (Ws) is anticipated by repetitively performing a prediction cycle comprising the following steps: • measuring (E1 to E5) the following magnitudes during a predetermined time interval: • a real speed of rotation of the rotary assembly at a given observation instant of said time interval; • at least one "fluid/turbine interaction" parameter that is representative of the interaction between the turbine and the drive fluid; and • at least one "fluid/rotary machine interaction" parameter that is representative of the interaction between the rotary machine and the driven fluid; • estimating the driving torque (Cm) applied by the turbine to the rotary assembly, on the basis of said real speed of rotation and of at least one "fluid/turbine interaction" parameter; • estimating, independently of estimating said driving torque (Cm), the resisting torque (Cr) applied by the rotary machine to the rotary assembly, from said real speed of rotation and said at least one "fluid/rotary machine interaction" parameter; • preparing (E9 to E12) a representative value (DC') that is representative of the difference between said driving torque (Cm) and said resisting torque (Cr); • calculating a predicted speed of rotation for the rotary assembly at a prediction instant later than said observation instant on the basis of said real speed of rotation, of said representative value (DC'), and of the time difference between the prediction instant and the observation instant; and • determining that a first condition is satisfied if said predicted speed of rotation exceeds the predetermined threshold speed (Ws); and in that an action is taken on the operation of the turbomachine in order to limit the extent to which the speed of its rotary assembly exceeds said threshold speed (Ws) in the event that, during the prediction cycle, it is determined that at least the first condition is satisfied. • measuring (E1 to E5) the following magnitudes during a predetermined time interval: • a real speed of rotation of the rotary assembly at a given observation instant of said time interval; • at least one "fluid/turbine interaction" parameter that is representative of the interaction between the turbine and the drive fluid; and • at least one "fluid/rotary machine interaction" parameter that is representative of the interaction between the rotary machine and the driven fluid; • a real speed of rotation of the rotary assembly at a given observation instant of said time interval; • at least one "fluid/turbine interaction" parameter that is representative of the interaction between the turbine and the drive fluid; and • at least one "fluid/rotary machine interaction" parameter that is representative of the interaction between the rotary machine and the driven fluid; • estimating the driving torque (Cm) applied by the turbine to the rotary assembly, on the basis of said real speed of rotation and of at least one "fluid/turbine interaction" parameter; • estimating, independently of estimating said driving torque (Cm), the resisting torque (Cr) applied by the rotary machine to the rotary assembly, from said real speed of rotation and said at least one "fluid/rotary machine interaction" parameter; • preparing (E9 to E12) a representative value (DC') that is representative of the difference between said driving torque (Cm) and said resisting torque (Cr); • calculating a predicted speed of rotation for the rotary assembly at a prediction instant later than said observation instant on the basis of said real speed of rotation, of said representative value (DC'), and of the time difference between the prediction instant and the observation instant; and • determining that a first condition is satisfied if said predicted speed of rotation exceeds the predetermined threshold speed (Ws);