The origin of pressure oscillations unique to divided chamber engines, and present even in the absence of knocking, is investigated theoretically with two-dimensional and zero-dimensional combustion models. It is found that, with ignition in the prechamber, if the prechamber pressure increases significantly over a time short in comparison to the acoustic time of the main chamber, a pressure imbalance between the two chambers results and finite-amplitude compression and expansion waves are generated from the throat region. The amplitude of the resulting oscillations, and the rate at which they decay, depend on the maximum value of the pressure difference (or of the throat Mach number) and on the strength and extent of the first, main-chamber compression wave. Such quantities in turn depend on the engine design and operating conditions in a complex manner due to the muhidimensionality, unsteadiness, and nonlinearity of the flowfield. Accordingly, simple universal trends are not obtained. However, it is concluded that higher-amplitude oscillations are obtained with higher engine speeds (but not necessarily monotonically) and faster prechamber combustion rates that in turn are related to the geometry of the prechamber, the spark location, and the flame speed. The amplitude also increases with decreasing throat area and increasing prechamber volume, but maxima are reached. At each point of the operating range, there are also optimal spark timings tor minimum oscillations.