S.Duzhin Infinitesimal Classification of First Order Systems of Two Partial Differential Equations In Two Variables. We give a classification of symbols of partial differential systems that consist of two equations imposed on two functions in two independent variables, with respect to the natural action of the group of linear changes of dependent and independent variables. The classification turns out to be finite, consisting of 5 types in the real case and of 4 types in the complex case. Apart from the elliptic, parabolic and hyperbolic types constituting the well-known classification of second order equations for a function $u(x,y)$, in the present case we also have two non-equivalent degenerate types.