The present invention relates to a method and a system for monitoring the following of a reference trajectory by an aircraft. The values that flight parameters of the aircraft will have on completion of a time interval .DELTA.T are extrapolated, the time interval .DELTA.T corresponding to a duration less than the remaining duration of validity of a guidance instruction presently applied by the aircraft and during which the instruction remains unchanged, by measuring at the start of the time interval .DELTA.T the actual values of the flight parameters as well as external conditions on which the performance of the aircraft depends, then by making the assumption that the instruction values of the flight parameters will remain constant throughout the time interval .DELTA.T, an alarm being raised if the extrapolated values of the flight parameters are not substantially equal to theoretical values of the flight parameters deduced from the reference trajectory on completion of the time interval considered .DELTA.T or if they are not compatible with the actual performance of the aircraft having regard to the measured external conditions.