  We investigate valued fields which admit a valuation basis. Given a countable
ordered abelian group G and a real closed, or algebraically closed field F, we
give a sufficient condition for a valued subfield of the field of generalized
power series F((G)) to admit a K-valuation basis. We show that the field of
rational functions F(G) and the field F(G) of power series in F((G)) algebraic
over F(G) satisfy this condition. It follows that for archimedean F and
divisible G the real closed field F(G) admits a restricted exponential
function.
