We develop an analytic theory based on an earlier model of the admittance of a ballistic transit time diode terahertz oscillator with tunnel emission of electrons into a transit space. The focus of this work is on the actual case when electrons are injected with high enough energy to move from the start with maximal (saturated) ballistic velocity (∼1×108 to 2×108 cm/s). On the one hand, such diodes have maximal oscillation frequencies and, on the other hand, a simple analytic theory describes them and allows us to avoid a cumbersome numerical procedure, which characterizes the general case. Such a description is analogous to the description of oscillatory diodes with diffusive transport and saturated drift velocity. We have also considered a special case when a small part of the ballistic electrons crossing the transit space scatter into a diffusive subsystem with a small drift velocity. The appearance of such slow-drifting electrons substantially increases space charge in the transit space and influences the static JV-characteristic but the high-frequency admittance is almost invariable.