Optoelectronic properties of some red mercuric iodide (alpha-HgI2) crystals have been studied for wavelengths 450-700 nm at temperatures 80-300 K. These crystals were grown (a) by solvent evaporation from alpha-HgI2-tetrahydrofurane saturated solution, (b) by hydration of alpha-HgI2-dimethyl sulphoxide-methanol saturated solution and (c) by polymer controlled growth (PCG) in vapour phase. Important aspects of optical generation of the charge carriers have been discussed. The measurements of thermally stimulated currents were also carried out in order to understand the temperature dependence of photocurrents in different wavelength regions. With the computer simulation of the photocurrent versus wavelength spectrum, the room temperature transport properties (the mobility-lifetime products and surface recombination velocities of the two charge carriers) for the crystals of three types have been estimated. For a typical electric field strength of about 2x10(3) V/cm, the electron drift lengths for the crystals of three types were found to be 1150, 1350 and 6500 mum, respectively, whereas the hole drift lengths were found to be 50, 50 and 150 mum, respectively. As the typical thickness of alpha-HgI2 photodetector for any scintillation spectrometer is about 300 mum, under the negative electrode illumination, all the three types of alpha-HgI2 crystals present high potential for their use as photodetectors in conjunction with most of the scintillators.