Disclosed herein are pyrazole derivatives which are represented by the following formula (I): ##STR1## wherein R.sup.1 represents a C.sub.1 -C.sub.4 alkyl group or a benzyl group; R.sup.2 represents a hydrogen atom or a C.sub.1 -C.sub.4 alkyl group; X represents a hydrogen atom, a halogen atom or a C.sub.1 -C.sub.4 alkyl group; R.sup.2 may combine with X to form ##STR2## wherein R.sup.5 represents a hydrogen atom or a C.sub.1 -C.sub.3 alkyl group; R.sup.3 represents a hydrogen atom or a C.sub.1 -C.sub.4 alkyl group; R.sup.4 s independently represent a hydrogen atom, a halogen atom, a C.sub.1 -C.sub.5 alkyl group, a C.sub.1 -C.sub.4 alkoxy group, a C.sub.1 -C.sub.4 alkylthio group, a trifluoromethyl group, a C.sub.1 -C.sub.4 haloalkoxy group, a phenyl group, an alkyl-substituted phenyl group or ##STR3## wherein Y represents an oxygen atom or a sulfur atom, R.sup.6 s independently represent a hydrogen atom, a C.sub.1 -C.sub.4 alkyl group, a C.sub.1 -C.sub.4 alkoxy group, a halogen atom, a nitro group, a cyano group or a trifluoromethyl group and n represents 1 or 2, adjacent R.sup.4 s being able to combine together to form ##STR4## wherein R.sup.7 represents a hydrogen atom or a methyl group; l represents 0 or 1; and m represents 1, 2, or 3. The pyrazole derivatives of the formula (I) show a high activity suitable for active ingredient of insecticidal and miticidal composition as well as fungicidal composition.