The Beilinson-Drinfeld's Grassmannian on an algebraic curve is an important object in Representation Theory and in the Geometric Langlands Program. I will describe some analogues of this construction when the curve is replaced by a surface, together with related preliminary results. This is partly joint work with Benjamin Hennion (Orsay) and Valerio Melani (Florence), and partly joint work in progress with Andrea Maffei (Pisa) and Valerio Melani (Florence).