I will report on work in progress with Marcello Mamino. Krapp observed that the residue field of an o-minimal EXP field has an induced exponential map making it into a model of T(exp) (the complete theory or the real exponential field). Assuming Schanuel's conjecture and using ideas of Wilkie, we show that this residue structure embeds into the original structure, so in particular SC implies that every o-minimal EXP-field has an archimedean substructure. Motivated by the quest for a natural axiomatization of T(exp). we then discuss the question of whether this substructure is elementary.