In the past few years, the price of petroleum based fuels, especially vehicle fuels such as gasoline and diesel, has been increasing at a significant rate. Consequently, there is much more consumer interest related to reducing fuel consumption for conventional vehicles and hybrid electric vehicles (HEVs) than in the past. The goal of many competitions and challenges held in North America and Europe is to achieve extremely low fuel consumption. A possible strategy to reduce fuel consumption is to use the vehicle's fuel converter such as an engine to accelerate the vehicle to a high speed and coast to a lower speed with the engine off. This method will reduce fuel flow to zero during the coast phase. Also, the vehicle uses higher power engine load to accelerate to the upper vehicle speed in a limited time, thus increasing the engine brake thermal efficiency. This strategy is known as "pulse and glide" or "burn and coast" in some references. In this study, the "pulse and glide" (PnG) method is first applied to a conventional vehicle to quantify the fuel consumption benefits when compared to steady speed conditions over the same distance. After that, an HEV is used as well to investigate if a hybrid system can further reduce fuel consumption with the proposed strategy. Note that the HEV used in this study has the advantage that the engine can be automatically shut off below a certain speed (~40 mph) at low loads, however a driver must shut off the engine manually in a conventional vehicle to apply this driving strategy. In this document, three preliminary results of the PnG driving strategy are presented; (1) improved fuel economy for a conventional vehicle from a simple spread sheet model, (2) improved fuel economy for an HEV from a dynamic vehicle simulation model (the Powertrain Analysis Toolkit (PSAT)) and (3) improved fuel economy for an HEV from vehicle testing at Argonne National Laboratory (ANL), all compared to steady speed conditions. The preliminary results show that the impact of engine load and kinetic energy stored in vehicle inertia is significant for fuel consumption using a PnG driving strategy compared to steady speed driving at the same average speed case. Especially, fuel economy can be improved at low speed range and higher acceleration because the aerodynamic drag force is smaller at low speed and the engine is running in a more efficient region for a short period of time respectively. In the last section, proposed directions of research are addressed based on the preliminary results. / Ph. D.