Discussions were given on features of various kinds of coal liquefaction catalysts exhibited by them in hydrocracking of coal (Taiheiyo coal), and particularly on selectivity of the reaction in its initial stage. Four kinds of catalysts were tested: Adkins catalyst which is an oxide of copper and chromium, Fe2O3+S, Mo-TiO2 and MoS3-Al2O3. Three grams of coal and 0.3 gram each of the catalysts were charged into an autoclave reactor and experiment was conducted under an initial hydrogen pressure of 10 MPa, temperatures from 653 K to 693 K and for durations of 0 to 120 minutes to derive apparent reaction rate constants. The MoS3-Al2O3 catalyst has promoting the reaction apparently in the primary reaction at any temperature, while the other catalysts had the rate constants varied in the initial and the later stages. It was recognized that the temperature dependence of rate constants varies considerably according to the types of catalyst. Particularly the MoO3-TiO3 catalyst has small temperature dependence in the rate constants, and high molecular weight reducing power. 3 refs., 4 figs., 3 tabs.