In this paper, we investigate the iterated order of solutions of higher order homogeneous and nonhomogeneous linear differential equations \begin{equation*} A_{k}eft( z\right) f^{eft( k\right) }+A_{k-1}eft( z\right) f^{eft( k-1\right) }+\cdots +A_{1}eft( z\right) f^{rime }+A_{0}eft( z\right) f=0 \end{equation*} and \begin{equation*} A_{k}eft( z\right) f^{eft( k\right) }+A_{k-1}eft( z\right) f^{eft( k-1\right) }+\cdots +A_{1}eft( z\right) f^{rime }+A_{0}eft( z\right) f=Feft( z\right) , \end{equation*} where $A_{0}\left( z\right) \not\equiv 0,A_{1}\left( z\right) ,\cdots ,A_{k}\left( z\right) \not\equiv 0$ and $F\left( z\right) \not\equiv 0$ are entire functions of finite iterated $p-$order. We improve and extend some results of He, Zheng and Hu; Long and Zhu by using the concept of the iterated order and we obtain general estimates of the iterated convergence exponent and the iterated $p$-order of solutions for the above equations.