Let $L = -/Delta + V$ be a Schr/"dinger operator where the nonnegative potential $V$ belongs to some appropriate reverse H/"older class. Consider the BMOspace associated to the Schr/"odinger operator $L$.In this talk we will characterise this BMO spaces using a condition of Carleson type.This result extends the  analogous characterization founded by Fabes, Johnson and Neri for the classical BMO space of John-Nirenberg. This is joint work with Lixin Yan and Chao Zhang.