A fuel system for an injection valve that introduces a liquid fuel and a gaseous fuel separately and independently of each other into a combustion chamber of an internal combustion engine, the fuel system comprising: a liquid fuel supply; a gaseous fuel supply; a liquid fuel pumping apparatus in fluid communication with the liquid fuel supply and supplying the liquid fuel to the injection valve at a pressure suitable for injecting the liquid fuel into the combustion chamber; a variable pressure regulator in fluid communication with the gaseous fuel supply and operable to adjustably regulate the gaseous fuel pressure, and supplying the gaseous fuel to the injection valve at a pressure suitable for injecting the gaseous fuel into the combustion; a first pressure sensor for measuring liquid fuel pressure downstream from the liquid fuel pumping apparatus; a second pressure sensor for measuring gaseous fuel pressure downstream from the pressure regulator; and a controller operatively connected with the liquid fuel pumping apparatus, the pressure regulator, the first pressure sensor and the second pressure sensor, and programmed to: monitor pressure signals from the first pressure sensor and the second pressure sensor that are representative of liquid fuel pressure and gaseous fuel pressure respectively; and command the liquid fuel pumping apparatus and the pressure regulator such that a target pressure differential between the liquid fuel pressure and the gaseous fuel pressure is maintained within a predetermined range of tolerance, characterized in that the target pressure differential is a function of engine operating conditions, wherein The target pressure differential is reduced at lower load engine operating conditions compared to higher load engine operating conditions. a liquid fuel supply; a gaseous fuel supply; a liquid fuel pumping apparatus in fluid communication with the liquid fuel supply and supplying the liquid fuel to the injection valve at a pressure suitable for injecting the liquid fuel into the combustion chamber; a variable pressure regulator in fluid communication with the gaseous fuel supply and operable to adjustably regulate the gaseous fuel pressure, and supplying the gaseous fuel to the injection valve at a pressure suitable for injecting the gaseous fuel into the combustion; a first pressure sensor for measuring liquid fuel pressure downstream from the liquid fuel pumping apparatus; a second pressure sensor for measuring gaseous fuel pressure downstream from the pressure regulator; and a controller operatively connected with the liquid fuel pumping apparatus, the pressure regulator, the first pressure sensor and the second pressure sensor, and programmed to: monitor pressure signals from the first pressure sensor and the second pressure sensor that are representative of liquid fuel pressure and gaseous fuel pressure respectively; and command the liquid fuel pumping apparatus and the pressure regulator such that a target pressure differential between the liquid fuel pressure and the gaseous fuel pressure is maintained within a predetermined range of tolerance, characterized in that the target pressure differential is a function of engine operating conditions, wherein monitor pressure signals from the first pressure sensor and the second pressure sensor that are representative of liquid fuel pressure and gaseous fuel pressure respectively; and command the liquid fuel pumping apparatus and the pressure regulator such that a target pressure differential between the liquid fuel pressure and the gaseous fuel pressure is maintained within a predetermined range of tolerance, characterized in that the target pressure differential is a function of engine operating conditions, wherein The target pressure differential is reduced at lower load engine operating conditions compared to higher load engine operating conditions.