  Let X be a non-singular algebraic curve of genus at least 3 and let M denote
the moduli space of stable vector bundles of rank n and fixed determinant of
degree d with n and d coprime. For any semistable bundle E over X, we can pull
E back to XxM, tensor with a universal bundle and take the direct image W(E) on
M. If the degree of E is sufficiently large, this direct image is locally free
and we call it a generalised Picard bundle. In this paper we prove an inversion
formula allowing us to recover E from W(E) and compute the space of
infinitesimal deformations of W(E). We also identify a family of deformations
which is locally complete and frequently globally complete as well. The paper
as a whole is a generalisation of results of Kempf and Mukai on Picard bundles
over the Jacobian of X.
