  In this paper we consider the dynamic pressure in a deep-water extreme Stokes
wave. While the presence of stagnation points introduces a number of
mathematical complications, maximum principles are applied to analyse the
dynamic pressure in the fluid body by means of an excision process. It is shown
that the dynamic pressure attains its maximum value beneath the wave crest and
its minimum beneath the wave trough, while it decreases in moving away from the
crest line along any streamline.
