We consider systems of formally hyperbolic differential equations in two complex variables and mappings described by differential operators between the solutions of such systems. First we transform these systems to a reduced form and give differential operators of order one. With this we can construct special differential operators of arbitrary order which map holomorphic functions into the set of solutions. As an application we construct a system of differential equations which is in close connection to the iterated differential equation of the generalized axially symmetric potential theory. For this system the Riemann-matrix-function is given also.