The neural baroreflex, which regulates mean arterial pressure (MAP) via the action of the brain, consists of baroreceptors which measure MAP, and actuators that can produce a change in MAP, such as the heart and parts of the peripheral resistance containing innervated smooth muscle. The brain is the controlling unit, maintaining an appropriate MAP in spite of various disturbances. Under certain circumstances, including haemorrhage and other states of distress, the gain of the neural baroreflex can change, causing low frequency (LF) oscillations (sometimes termed Mayer waves) in blood pressure (BP). Though their purpose is unclear, the origins of these LF oscillations has previously been explained via a nonlinear feedback model, though focusing on the peripheral resistance as an MAP actuator only. The present paper now includes analytical and simulation results explaining the LF oscillation phenomenon for the full neural baroreflex, containing both peripheral resistance (PR) and cardiac branches. However, the main contribution of the paper is to examine the effect of blood pulsatility, or a lack of pulsatility, on the neural baroreflex, and how it's effect can manifest in the presence of LF oscillations. This may have importance in cases where pulsatility is reduced (for example where left-ventricular assist devices are present), or completely absent (for example in turbine-based artificial hearts).