The strongly mismatched semiconductors in the form of cadmium sulfide and cadmium telluride were used in the fabrication, by the solid-phase substitution reaction method, of a series of heterojunctions with a low density of the surface states N(s) almost-equal-to 3 X 10(11) cm-2. It was established that in the case of heterojunction diodes with the barrier width d0 = 0.3-0.5-mu-m the forward current flowing at low bias voltages is due to the tunneling of the thermally excited electrons, whereas in samples with d0 = 0.5-1.0-mu-m this current is due to the recombination of carriers in the space charge region. Under high forward bias voltages the current is of thermionic nature. The reverse current in such structures is due to the tunnel effect. In the case of samples with d0 greater-than-or-similar-to 1-mu-m the current-voltage characteristics are governed by the space-charge-limited current. The structures have a photoconversion efficiency of 0.7-0.8 electrons/photon in the spectral range 1.3-2.3 eV. The practical applications of such heterojunctions are considered.