Let \(N\) be a manifold together with a transitive action of the Lie group \(G\) and \(M\) be any smooth manifold with \(\dim M= \dim N\). The author calls a free \((N,G)\)-coframe of order \(k\) at a point \(x\in M\) the \(k\)-jet of a local diffeomorphism \(\varphi: M\to N\) at this point and denotes by \(R^ k (M)\) the space of all free \(k\)-coframes. The Lie group \(G\) acts in a natural way in the fiber bundle of free coframes. By a homogeneous \((N,G)\)-structure on a manifold \(M\) he means a subbundle \(E_ k\subset R^ k(M)\) which is the principal \(G\)-bundle with respect to the action of the group \(G\) in the space \(R^ k(M)\). In the paper under review, the author considers some properties of such structures related to systems of differential equations, Cartan connection and its curvature.