  Deformations of topological open string theories are described, with an
emphasis on their algebraic structure. They are encoded in the mixed
bulk-boundary correlators. They constitute the Hochschild complex of the open
string algebra -- the complex of multilinear maps on the boundary Hilbert
space. This complex is known to have the structure of a Gerstenhaber algebra
(Deligne theorem), which is also found in closed string theory. Generalising
the case of function algebras with a B-field, we identify the algebraic
operations of the bulk sector, in terms of the mixed correlators. This gives a
physical realisation of the Deligne theorem. We translate to the language of
certain operads (spaces of d-discs with gluing) and d-algebras, and comment on
generalisations, notably to the AdS/CFT correspondence. The formalism is
applied to the topological A- and B-models on the disc.
