On differential invariants of geometric structures

We prove that if the fibre dimension $m$ of a bundle of geometric structures exceeds the dimension $n$ of its base, then the number of sufficiently general functionally independent local differential invariants of the bundle increases to infinity as the differential degree of these invariants grows. For $m\le n$ we describe all but two canonical forms to which every sufficiently general geometric structure can be reduced by an appropriate coordinate change on the base. The results obtained may be generalized.