Substituted pyrazole compounds represented by formula (I), or salts thereof are disclosed, wherein R.sup.1 is --CH(OH)--CH(R.sup.4)-(A).sub.n-Y, --CH.sub.2--CH(R.sup.4)-(A).sub.n-Y, --CO-B.sup.1-A-Y or the like (wherein A is a lower alkylene; Y is an aryl group which may be substituted, for example, by halogen, or the like; R.sup.4 is a hydrogen atom or a lower alkyl group; B.sup.1 is --CH(R.sup.4)-- or --N(R.sup.4)--; and n is 0 or 1); R.sup.2 is a hydrogen atom, a lower alkyl group which may be substituted by hydroxyl or the like, or an aralkyl group; R.sup.3 is a phenyl group which may be substituted by halogen or the like, or a pyridyl group; and Q is a pyridyl or quinolyl group. These substituted pyrazole compounds or their salts have an excellent p38MAP kinase inhibiting effect and are hence useful in the prevention or treatment of tumor necrosis factor .alpha.-related diseases, interleukin 1-related diseases, interleukin 6-related diseases or cyclooxygenase II-related diseases ##STR00001##