[en] It was in particular recently argued that the gauge theory in the presence of a certain one-parameter deformation can at low energies effectively be described in terms the quantization of an algebraically integrable system, which is canonically associated to this theory. It seems, however, that the deeper reasons for this relationship between a two- and a fourdimensional theory remain to be understood. A clue in this direction may be seen in the fact that the instanton partition functions which represent the building blocks of the partition functions are obtained by specializing a two-parameter family Z(a,ε₁,ε₂;q) of instanton partition functions. These functions were identified with the conformal blocks of Liouville theory. This indicates that the relationship between certain gauge theories and Liouville theory involves in particular a two-parametric deformation of the algebraically integrable model associated to the gauge theories on R⁴ which ultimately produces Liouville theory as a result. One of my intentions in this paper is to clarify in which sense this point of view is correct. Another piece of motivation comes from relations between fourdimensional gauge theories and the geometric Langlands correspondence. The author feels that the mentioned relations between gauge theory and conformal field theory offer new clues in this regard. It is therefore my second main aim to clarify the relations between the quantization of the Hitchin system, the geometric Langlands correspondence and the Liouville conformal field theory. (orig.)