The objective of this paper is to illustrate the benefits of the influence of the steam and oxyhydrogen gas (HHO) on the composition of emitted exhaust gases and energy usage of operating the internal combustion engine (ICE) that drives a generator-powered battery electric vehicle (BEV). The employed internal combustion generating sets can be used as trailer mounted electric energy sources allowing one to increase the range of BEV vehicles, mainly during long distance travel between cities. The basic configurations of hybrid and electric propulsion systems used in a given Electric Vehicles (xEV) includes all types of Hybrid Electric Vehicles (xHEV) and Battery Electric Vehicles (xBEV), which are discussed. Using the data collected during traction tests in real road traffic (an electric car with a trailer range extender (RE) fitted with ICE generators (5 kW petrol, 6.5 kW diesel), a mathematical model was developed in the Modelica package. The elaborated mathematical model takes into account the dynamic loads acting on the set of vehicles in motion and the electric drive system assisted by the work of RE. Conducted tests with steam and HHO additives for ICE have shown reduced (5–10%) fuel consumption and emissions (3–19%) of harmful gases into the atmosphere.