Terahertz cyclotron-resonance photoconductivity in a two-dimensional electron-hole system under conditions where the cyclotron resonance occurs owing to the absorption of radiation by electrons whose density is one to three orders of magnitude lower than the hole density is experimentally investigated for the first time. Information on the behavior of the main parameters (i.e., amplitude and broadening) characterizing resonance photoconductivity as a function of wavelength, temperature, and electron density is obtained. On this basis, it is concluded that resonance photoconductivity in the system under study results from cyclotron resonance caused by transitions between the partially filled zeroth Landau level and the first Landau level of electrons, and resonance broadening is caused by scattering on a short-range screened impurity potential. It is found that a decrease in the electron density by an order of magnitude does not lead to a significant reduction of the photoconductivity signal; moreover, at a wavelength of 432 m, the signal even grows slightly. This fact can be associated with the effective enhancement of the field of the incident radiation in the system under study.