A theory of magnetization dynamics in ferrimagnetic materials with antiparallel aligned spin sublattices under the action of spin-transfer torques (STTs) is developed. In contrast with antiferromagnets, the magnetic sublattices in ferrimagnets are formed by different magnetic ions, which results in a symmetry breaking in the dynamic equations for Néel’s vector. We demonstrate that this symmetry breaking becomes crucially essential for the THz signal extraction in ferrimagnetic spin-torque oscillators. As an example, we consider magnetization dynamics in GdFeCo layers in spin Hall and nanocontact spin-torque oscillator geometries. We demonstrate that (i) the application of spin current leads to a conical precession of Néel’s vector with sub-THz frequencies, (ii) in the spin Hall geometry, the conical precession leads to sub-THz oscillations of the Hall voltage, and (iii) in the nanocontact geometry the Néel’s vector precession leads to sub-THz oscillations of the magnetoresistance.