A fuel distillation property determining apparatus for use in a multi-injection system for diesel engines. The apparatus acquires a physical quantity indicating a state of burning of fuel in the diesel engine, determines a physical quantity variation sensitivity defined by a ratio of a quantity variation that is a difference between a first value of the physical quantity, as acquired upon execution of a first one of a sequence of sub-injections, and a second value of the physical quantity, as acquired upon execution of a following one of the sub-injections, to a difference between a first quantity of fuel sprayed in the first sub-injection and a second quantity of fuel sprayed in the following sub-injection, and determine a cetane value of the fuel based on a predefined relation between the physical quantity variation sensitivity and the cetane value. This ensures the accuracy in determining the cetane value at low costs.