This work is devoted to the study of the inhibition of corrosion of mild steel (MS) in molar hydrochloric acid (1 mol.L-1 HCl) by two named quinoxaline derivatives namely, 2-(2,4-dichlorophenyl)-1,4-dihydroquinoxaline (HQ) and 2-(2,4-dichlorophenyl)-6-methyl-1,4-dihydroquinoxaline (CQ). The inhibitory efficacy of HQ and CQ compounds is first evaluated using the gravimetric method and using electrochemical techniques (stationary and transient techniques). The results showed that our compounds are efficient corrosion inhibitors and the inhibition rates (eta(EIS)%) reached up to 91% and 94.2% at 10(-3) mol.L-1 for HQ and CQ respectively. The mentioned molecules are classified as mixed-type inhibitors. The adsorption of these inhibitors on the surface of steel in hydrochloric HCl mol.L-1 medium obeys the Langmuir adsorption isotherm. The results of the scanning electron microscope (SEM) showed the formation of a protective film on the surface of the steel in the presence of the inhibitors studied. Elementary analysis is obtained by energy dispersive X-ray spectroscopy (EDS). The inhibition property was further elucidated by theoretical approaches such as: Density Functional Theory (DFT), quantum chemical descriptors (QCD), local reactive indices, solvent effect, theoretical complexation, Molecular Dynamic (MD) simulation, effect of temperature on adsorption energy (E-ads), Radial Distribution Function (RDF), and Mean Square Displacement (MSD). The results of these approaches support the experimental results. (C) 2020 The Chemical Industry and Engineering Society of China, and Chemical Industry Press Co., Ltd. All rights reserved.