  Cluckers and Lipshitz have shown that real closed fields equipped with real
analytic structure are o-minimal. This generalizes the well-known subanalytic
structure $\mathbb{R}_{\mathrm{an}}$ on the real numbers. We extend this line
of research by investigating ordered fields with real analytic structure that
are not necessarily real closed. When considered in a language with a symbol
for a convex valuation ring, these structures turn out to be tame as valued
fields: we prove that they are $\omega$-h-minimal. Additionally, our approach
gives a precise description of the induced structure on the residue field and
the value group, and naturally leads to an Ax--Kochen--Ersov-theorem for fields
with real analytic structure.
