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Abstract Internal combustion engines (both spark ignition and compression ignition) are fuelled mostly with liquid fuels (petrol, diesel oil). Nowadays more and more the gaseous fuels (for instance: natural gas, coal bed methane, compressed natural gas (CNG), synthetic natural gas (SNG), liquid petroleum gas (LPG) and Biogas) are applied as driving fuel of internal combustion engines. In case of spark ignition engines, in which the ignition of the earlier prepared vaporised fuel-air mixture is realised by the strange spark ignition source, the liquid fuel (petrol) can be replaced totally without additional troubles by the gas fuels. This possibility in case of compression engines is essentially restricted, because ignitability of the gaseous fuels is mostly not so good as ignitability of the diesel oil. Self-ignition of the fuel gas appears only at considerable higher temperatures in comparison to self-ignition of classical diesel oil. Solution if this problem can be achieved by using of the dual fuel system. The diesel engine can be fulfilled with the fuel gas basically, but for ignition of the prepared fuel gas - air mixture a specified amount of the liquid fuel (diesel oil) should be additionally injected into the combustion chamber. Diesel engine working with the dual fuel system has to perform simultaneously the needed effective mechanical torque and power output. For assurance that the whole combustion process in the engine cylinder proceeds without mistakes and completely, some basic conditions should be satisfied. In the frame of this work, three main aspects of this problem are taken into account: a. filling of the engine cylinder, b. stoichiometry of the combustion process, c. performance of mechanical parameters (torque, power output, engine rotational speed). A complex theoretical analysis of these conditions connected with the dual fuel combustion process has been done and some results of the carried out investigations are presented in the paper. Keywords: fuelling of internal combustion engines, substitution of fuels, gas fuels, dual fuel system, efficiency.