The electrical characteristics of multilayer structures based on amorphous ultrathin diamondlike carbon films were investigated including dynamic and quasi-static current-voltage characteristics, capacitance-voltage characteristics, deep level transient spectra. The effect of illumination and temperature on these characteristics was also investigated. For the multilayer structures composed of lower band gap amorphous carbon layers separated with higher band gap ones, there were observed well-defined regions of negative differential resistance and sharp 20-fold changes in capacitance at definite voltages. Activation energies, capture cross sections, and locations of trapping centers were defined. The effects observed are discussed in terms of trap-assisted tunneling and, also, in terms of resonant tunneling between energy levels in superlattices and charge filling of the quantum wells and trapping centers.