  Liouville closed $H$-fields are ordered differential fields whose ordering
and derivation interact in a natural way and where every linear differential
equation of order $1$ has a nontrivial solution. (The introduction gives a
precise definition.) For a Liouville closed $H$-field $K$ with small derivation
we show: $K$ has the Intermediate Value Property for differential polynomials
iff $K$ is elementarily equivalent to the ordered differential field of
transseries. We also indicate how this applies to Hardy fields.
