Offset and its long-term stability is a weak point of fluxgate sensors. Even the ultrastable sensors kept at no vibrations and stable temperature at magnetic observatories show offset drift. Such drift of the fluxgate triaxial sensor can only be partly corrected by the scalar resonance magnetometer. Periodical calibration of absolute reading should be made using nonmagnetic theodolite. In this paper, we study the origin of fluxgate offset. We distinguish the real magnetic sensor offset from the offset contributions originating in the false second harmonics signal that leaks to the sensor output from the distortion in the excitation signal, or which is borne as harmonic distortion when the signal processing electronics are subjected to the large first harmonic signal leaking from the excitation. We analyze the offset dependence on the angular position of the sensor core and its response to large field shocks. The experiments give an indication that only a part of the magnetic offset stems from a remanence of magnetically hard core regions. The residual part may be caused by a magnetostrictive signal, belonging to false signal contributions, but not considered in previous studies.