Radio position-fixing systems employing the continuous-wave hyperbolic principle, such as the Decca Navigator and Loran C, are now used by ships and aircraft numbering tens of thousands and the theory of their operation has become part of the syllabus in many courses of instruction on navigational aids. Although accepting that these systems produce position-lines along which the difference in the distance from the user to a master and slave station is constant, and that such a line is obtained by time-difference measurement in the form of phase comparison between the two received signals, it may be asked whether this process is affected by the doppler frequency-shifts that will occur if the craft is moving with respect to the stations. Surely, the question goes, these must complicate or modify the behaviour of the system and give rise to an error unless the receiver is stationary ? It sometimes seems to come as a surprise to learn that, far from being adversely affected by it, the operation of these systems is a practical example of the phenomenon to which Prof. C. J. Doppler gave his name: they work not in spite of his ‘shift’, but because of it.