Let G be a finitely generated Fuchsian group of the second kind without any parabolic element and f be a univalent analytic function in the unit diskDcompatible withG. In this paper, westudy the higher order Schwarzian derivatives: ?n+1( f ) = ?? n( f )?(n?1) f?? f???n( f ), n ? 3, where ?3(f) stands for the Schwarzian derivatives of f, and Sn(f) = (f?) n?1/2 Dn( f ?)? n?1/2 , n ? 2. For p > 0, we show that if |?n(f)(z)|p(1?|z|2)p(n?1)?1dxdy (resp. |Sn( f )(z)|p(1 ? |z|2)pn?1dxdy) satisfies the Carleson condition on the infinite boundary of the Dirichlet fundamental domainF ofG, then |?n( f )(z)|p(1?|z|2)p(n?1)?1dxdy (resp. |Sn( f )(z)|p(1?|z|2)pn?1dxdy) is a Carleson measure in D. Similarly, for p > 0 and a bounded analytic function f in the unit disk D compatible with G, we prove that if | f ?(z)|p(1 ? |z|2)p?1dxdy satisfies the Carleson condition on the infinite boundary of the Dirichlet fundamental domain F of G, then |f?(z)|p(1 ? |z|2)p?1dxdy is a Carleson measure in D.