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The influence of ambient current fields on the mild-slope approximation is reassessed using theHamiltonian variational principle. Considering the slowly modulated non-uniform currents which may possess both verti-cal and horizontal variations, the extended mild-slope equation for surface waves propagating over slowly varying topogra-phy is derived. It is found that for large current velocities comparable to the wave celerity and the group velocity, the ex-tended mild-slope equation is valid. For the validity of the geometric optics-approximation, additional conditions con-cerning current fields should be satisfied.