  We study random relational structures that are \emph{relatively
exchangeable}---that is, whose distributions are invariant under the
automorphisms of a reference structure $\mathfrak{M}$. When $\mathfrak{M}$ has
{\em trivial definable closure}, every relatively exchangeable structure
satisfies a general Aldous--Hoover-type representation. If $\mathfrak{M}$
satisfies the stronger properties of {\em ultrahomogeneity} and {\em
$n$-disjoint amalgamation property} ($n$-DAP) for every $n\geq1$, then
relatively exchangeable structures have a more precise description whereby each
component depends locally on $\mathfrak{M}$.
