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 diskD compatible with G. In this paper, we study the higher order Schwarzian derivatives: σn+1( f ) = σ′n( f )−(n−1) f ′′ f ′ ·σn( f ), n ≥ 3,where σ3( f ) stands for the Schwarzian derivatives of f , and Sn( f ) = ( f ′) n−1 2 Dn( f ′)− n−12 , n ≥ 2. For p > 0, we show that if |σn( 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 of G, then |σn( 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.