  The purpose of this paper is to study the notion of relative extreme
amenability for pairs of topological groups. We give a characterization by a
fixed point property on universal spaces. In addition we introduce the concepts
of an extremely amenable interpolant as well as maximally relatively extremely
amenable pairs and give examples. It is shown that relative extreme amenability
does not imply the existence of an extremely amenable interpolant. The theory
is applied to generalize results of Kechris, Pestov and Todorcevic relating to
the application of Fra\"{i}ss\'e theory to the theory of Dynamical Systems. In
particular, new conditions enabling to characterize universal minimal spaces of
automorphism groups of Fra\"{i}ss\'e structures are given.
