THE CARTAN CONNECTION AS AN INVARIANT OF DIFFERENTIAL SYSTEM Glizburg Vita I Key words: Reductive connection; higher order frame bundle; system of arbitrary order differential equations. 1991 Math. Subject Classification: Primary 53C07; 53C05, 53C15, 53B20, 53B21. Abstract: We suggest the invariant geometric description of the system of ordinary arbitrary order differential equations achieved by the reduction of this system to the reductive Cartan connection in some naturally arising principal bundle.