A transient analysis simulation program is developed for studying the response of an indirect injection, naturally aspirated, diesel engine after a rapid increase in load when this is equipped with various types of indirect acting governors. Analytical expressions are presented for the better simulation of engine mechanical friction, inertia moments and heat loss to the walls under transient conditions, governor dynamics for both the sensing element and the servopiston, soot emissions and the fuel pump operation. Various types of governor sensing elements (i.e. mechanical, electrical, two-pulse) and feedbacks (i.e. unity and vanishing) for the servomechanism are studied. Explicit diagrams are given to show how each combination of governor type and technical parameters (i.e. mass and number of flyweights, geometrical dimensions, amplification factors) affects the speed response as well as the speed droop and the recovery period of the particular engine.