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.