This study develops the dynamic equations that describe the behavior of a hydrostatic transmission utilizing a variable-displacement axial-piston pump with a fixed-displacement motor. In general, the system is noted to be a third-order system with dynamic contributions from the motor, the pressurized hose, and the pump. Using the Routh-Hurwitz criterion, the stability range of this linearized system is presented. Furthermore, a reasonable control-gain is discussed followed by comments regarding the dynamic response of the system as a whole. In particular, the varying of several parameters is shown to have distinct effects on the system rise-time, settling time, and maximum percent-overshoot.