In this paper the combustion and ignition process,in the hydrogen-fueled peripheral ported rotary engine with single and dual laser ignition systems was studied numerically. The computational method was established for the process simulation including interaction between turbulence and chemical reactions. The detailed chemical kinetic model of hydrogen combustion was used. It was shown that the ignition and combustion process in the H-2-fueled rotary engine is highly transient with specific distortion and stretching of the combustion front in the combustion chamber due to complex motion of the rotor relative to the engine housing. The single and dual laser ignition systems were simulated to compare the ignition efficiency and the rate of hydrogen burning out. The evaluation of pressure in the combustion chamber was performed and compared with the experimental data obtained for the rotary engine fueled by natural gas. It was shown that the H-2-fueled rotary engine with the dual laser ignition system has potential application in alternative automotive industry due to high efficiency and near-zero carbon-based emission. (C) 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.