Electroconductive ceramic composites have many special applications for electronics, wireless communications and nuclear physics. In the latter case, additional requirements appear such as narrow range of conductivity, vacuum-tightness and decay of long-life isotopes. Multiwall carbon nanotubes (MWCNT)-Al2O3 composite ceramics can satisfy the conditions, if dense material is received. In this work, attempts to receive such material are made. Dependence of the conductivity on start particle size (0.1-1μm), methods of mixing (dry and wet) and consolidation (cold and hot isostatic techniques) are obtained and analyzed. Vacuum-tight (10-7 torr/l/s), dense (98%TD) composite material was sintered at 1520°C 200 MPa in hot isostatic press, having electroconductivity level 10-3 S/cm.