We have considered interactions between ballistic (or quasiballistic) electrons accelerated by a dc electric field in an undoped transit space (T space) and a small ultrahigh frequency ac electric field and have calculated the linear admittance of the T space. Electrons in the T space have a conventional, nonparabolic dispersion relation. After consideration of the simplest specific case when the current is limited by the space charge of the emitted electrons, we turned to an actual case when the current is limited by a heterostructural tunnel barrier (B barrier) separating the heavily doped cathode contact and the T space. We assumed that the B barrier is much thinner than the T space and both dc and ac voltages drop mainly across the T space. The emission tunnel current through the B barrier is determined by the electric field E(0) in the T space at the boundary B barrier/T space. The more substantial is, the tunnel current limitation the higher the electric field E(0) becomes. We have shown that for a space-charge limited current the change from parabolic dispersion to the nonparabolic branch induces narrowing and closing of the frequency windows of transit-time negative conductance starting with the lowest-frequency windows. These narrowing and closing frequency windows become effective only for very high voltages U across the T space: U≫mVS2/2e, where m is the effective mass for the parabolic branch and VS is the saturated velocity for the nonparabolic branch. For moderate voltages U, the effects of nonparabolicity are not very substantial. The tunnel current limitation decreases the space-charge effects in the T space and diminishes the role of the detailed electron dispersion relation. As a result, restoration of the frequency windows of transit-time negative conductance and an increase in the value of this negative conductance occur. The imple- mentation of the considered tunnel injection transit time oscillator diode promises to lead to efficient and powerful sources of terahertz range radiation. © 2003 American Institute of Physics.