In order to investigate the influence of small perturbations on the invariants of dynamical systems， we study the approximate Noether invariants of nonconservative systems under El-Nabulsi exponential model and El-Nabulsi power-law model. According to Hamilton’s principle with nonstandard Lagrangians as its action functional， the dynamics equations of El-Nabulsi type for nonconservative systems are established. On this basis， due to the invariance of the functional under infinitesimal transformation， the approximate Noether invariants of nonconservative systems under small disturbance are obtained. When not disturbed， the exact Noether invariants are given. The approximate Noether invariant theorems for nonconservative systems under El-Nabulsi exponential model and El-Nabulsi power-law model are proved. This method provides a new idea for the study of nonconservative system dynamics， and two examples show the effectiveness of the results.