  We study geometrical aspects of the space of fibrations between two given
manifolds M and B, from the point of view of Frechet geometry. As a first
result, we show that any connected component of this space is the base space of
a Frechet-smooth principal bundle with the identity component of the group of
diffeomorphisms of M as total space. Second, we prove that the space of
fibrations is also itself the total space of a smooth Frechet principal bundle
with structure group the group of diffeomorphisms of the base B.
