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We derive relativistic corrections for one-way and two-way time and frequencytransfer over optical fibres neglecting no terms that exceed 1 ps in time and$10^{-18}$ in fractional frequency, and estimate their magnitude in typicalfibre links. We also provide estimates of the uncertainties in the evaluationof the relativistic corrections due to imperfect knowledge of parameters likethe coordinates of the fibre and stations, Earth rotation, or thermal effectsof the fibre index and length. The links between Teddington(UK) and Paris(F) aswell as Braunschweig(D) and Paris(F), that are currently under construction,are studied as specific examples.

Relativistic Corrections for Time and Frequency Transfer in Optical Fibres