Abstract: It is well-known that the subanalytic structure on the real numbers is o-minimal. Cluckers and Lipshitz have shown that this remains true for elementary extensions of the reals equipped with certain nonstandard analytic functions. More precisely, if B is a real Weierstrass system, then any real closed field with B-analytic structure is o-minimal. In this talk, we consider B-analytic structure on ordered fields that are not necessarily real closed. Such structures cannot be o-minimal in general. Still, they turn out to be tame as valued fields: when equipped with a convex valuation, they give rise to new examples of ?-h-minimal structures. This talk is based on joint work with Kien Huu Nguyen and Floris Vermeulen.