Let
be a projective smooth irreducible polarized variety over the field of complex
numbers. Typical examples of wide extensions are vector bundles
that have a subsheaf
whose slope is much bigger than the slope of
, and such that
and
are stable. We study the deformations of such bundles. The case of unstable
rank 2 bundles has been considered by S.A. Strømme on
, and by C. Banica on
. We build moduli spaces of wide extensions, and if the dimension of
is greater than 2, it may even happen that we obtain fine moduli spaces.