  Let $X$ be a (smooth and complete) curve and $G$ a reductive group. In [BG]
we introduced the object that we called "geometric Eisenstein series". This is
a perverse sheaf $\bar{Eis}_E$ (or rather a complex of such) on the moduli
stack $Bun_G(X)$ of principal $G$-bundles on $X$, which is attached to a local
system $E$ on $X$ with respect to the torus $\check{T}$, Langlands dual to the
Cartan subgroup $T\subset G$. In loc. cit. we showed that$\bar{Eis}_E$
corresponds to the $\check{G}$-local system induced from $E$, in the sense of
the geometric Langlands correspondence.
  In the present paper we address the following question, suggested by V.
Drinfeld: what is the perverse sheaf on $Bun_G(X)$ that corresponds to the
universal deformation of $E$ as a local system with respect to the Borel
subgroup $\check{B}\subset \check{G}$?
  We prove, following a conjecture of Drinfeld, that the resulting perverse
sheaf if the classical, i.e., non-compactified Eisenstein series.
