The electro-optical response and the microstructure of multiwalled carbon nanotubes dispersed in nematic liquid crystals with negative dielectric anisotropy are investigated. In contrast to undoped liquid crystals, the liquid crystal dispersions of carbon nanotubes are characterized by the irreversible electro-optic response or the so-called electro-optical memory effect. This effect is that the light transmittance through the sandwiched layer of the dispersion placed between two crossed polarizers considerably increases after the electric field application. cycle. The state of memory persisted over months of our observation. The memory is caused by the incomplete relaxation of liquid crystal molecules from the random planar to the initial homeotropic state after the field is off. It is pointed out that the stabilization of the planar state is due to the network of small nanotube aggregates formed in the liquid crystal disturbed by electro-hydrodynamic flows. It is revealed that the efficiency of electro-optical memory depends on the network morphology and the efficiency of electro-hydrodynamic flows in a liquid crystal.