  We define the infinitesimal and geometric orders of an effective Klein
geometry G/H. Using these concepts, we prove i) For any integer m>1, there
exists an effective Klein geometry G/H of infinitesimal order m such that G/H
is a projective variety (Corollary 9). ii) An effective Klein geometry G/H of
geometric order M defines a differential equation of order M+1 on G/H whose
global solution space is G (Proposition 18).
