In this paper, we investigate the iterated order of solutions of higher order nonhomogeneous linear differential equations Ak (z) ƒ (k)+Ak-1 (z) ƒ (k-1)+ … +A1 (z) ƒ’+A0 (z) ƒ = F (z), where A0 (z), A1 (z), … , Ak (z) ( 0 are entire functions of finite iterated p-order and F (z) is entire function of infinite iterated p-order. We improve and extend some recent results of Chen and we obtain general estimates of the iterated convergence exponent, the iterated p-order and the iterated convergence exponent of arbitrary order derivatives of the solutions of the above equation.