Valuation bases for generalized algebraic series fields

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 with subfield K, 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.