Monotone T-convex T-differentialfields

Let T be a complete, model complete o-minimal theory extending the theory of real closed ordered fields and assume that T is power bounded.Let K be a model of T equipped with a T -convex valuation ring O and a T -derivation such that is monotone, i.e., weakly contractive with respect to the valuation induced by O.We show that the theory of monotone T -convex T -differential fields, i.e., the common theory of such K , has a model completion which is complete and distal.Among the axioms of this model completion, we isolate an analogue of henselianity that we call T -henselianity.We establish an Ax-Kochen/Ershov theorem and further results for monotone T -convex T -differential fields that are T -henselian.