The present invention relates to a novel 1,2,4-thiadiazole compound represented by the formula (1): ##STR00001## wherein, R.sup.1 represents C3-C7 alkynyl that may be substituted with halogen atom; R.sup.2 represents C3-C8 cycloalkyl which may be substituted with C1-C4 alkyl, halogen atom and trifluoromethyl or the like; A.sup.1 represents a single bond, C1-C2 alkylene or C2-C3 alkylidene. The 1,2,4-thiadiazole compound has an excellent arthropod controlling activity, and can effectively control an arthropod pests such as insect pests, acarine pests and the like.