  This article is devoted to the investigation of semidirect products of groups
of loops and groups of diffeomorphisms of finite and infinte dimensional real,
complex and quaternion manifolds. Necessary statements about quaternion
manifolds with quaternion holomorphic transition mappings between charts of
atlases are proved. Unitary representations of these groups including
irreducible are constructed with the help of stochastic processes and
quasi-invariant transition measures on groups $G$ relative to dense subgroups
$G'$. It is proved, that this procedure provides a family of the cardinality
$card ({\bf R})$ of pairwise nonequivalent irreducible unitary representations.
A differentiability of such representations is studied.
