An embodiment of the invention is a composition of diesel, biodiesel or blended fuel (DF) with exhaust gas (EG) mixtures or with liquid CO.sub.2. The composition is in a liquid state near the supercritical region or a supercritical fluid mixture such that it quasi-instantaneously diffuses into the compressed and hot air as a single and homogeneous supercritical phase upon injection in a combustion chamber. Suitable temperatures and pressures are greater than about 300.degree. C. and 100 bar, and the mole fraction of EG or CO.sub.2 (X.sub.EG or X.sub.CO2) in DF is in the range of 0.0-0.9. In a combustion process embodiment, composition embodiments are injected into a combustion chamber under supercritical conditions. The content of EG or CO.sub.2 in DF can be controlled as a function of engine operating parameters such as rpm and load. The thermodynamic and transport properties of supercritical DF-EG or DF-CO.sub.2 compositions can be more easily tuned and controlled than subcritical two-phase compositions. Delivery of the DF-EG or DF-CO.sub.2 composition into the combustion chamber as a homogeneous isotropic single-phase composition provides a significant increase in engine efficiency. Combustion process and fuel system embodiments of the invention provide an improved composition process with reduced formation of particulate matter (PM), aldehydes, polyaromatic hydrocarbons (PAHs), CO, NO.sub.x, and SO.sub.x.