Nitriding and carburizing are important methods to strengthen the surface of iron-based alloys. Addition of rare earth (RE) during nitriding or carburizing will reduce processing time, increase thickness, improve microstructures and mechanical properties of modified surface layers. There are extensive applications for RE-nitriding and RE-carburizing in experimental researches and industrial manufacture. However, the researches on RE catalyzing during nitriding or carburizing on iron-based alloys are seldom reported. Therefore, first-principles calculations are employed to investigate RE-nitrided and RE-carburized layers on iron-based alloys in this work. Our investigations focus on solid solution and surface of bcc Fe with alloying elements such as C, N, La. Our calculated results are summarized as follows. (1) The concentration gradient of C (or N) + the repulsion of FIAs = the resultant force towards core of C (or N) atoms. The resultant force towards core is the diffusion driving force of N (or C) atoms in iron-based alloy. (2) The RE catalyzing mechanism is discovered. i. The diffusion driving force of N (or C) atoms is enhanced. The diffusion driving force of N (or C) atoms in RE-nitriding (or RE-carburizing) is the repulsion of N (or C) atoms + the La-N (or -C) repulsion. ii. The implantation of N (or C) atoms into the iron surface due to RE adsorption. iii. The RE catalyzing anti-trap theory is developed. The octahedral interstitials are the traps of N (or C) atoms. An anti-trap zone around a RE atom is formed due to the La-N (or -C) repulsion. Because of the existence of many anti-trap zones, the concentration of N (or C) increases rapidly. Furthermore, the increase of N (or C) concentration gradient accelerates the diffusion of N (or C) atoms. In our investigations, the RE catalyzing of RE-nitriding (or -carburizing) is proposed. This work is beneficial to the technological innovation of RE-nitriding (or -carburizing), design, preparation and application of RE-doped and modified new materials. Our calculation results and proposed theory are of significance to theoretical studies and applications.