Arachidonic acid (ARA) and docosahexaenoic acid (DHA), which are the dominant polyunsaturated fatty acids in the brain, have crucial roles in brain development and function. Recent studies have shown that ARA and DHA promote postnatal neurogenesis. However, the direct effects of ARA on neural stem/progenitor cells (NSPCs) and the effects of ARA and DHA on NSPCs at the neurogenic and subsequent gliogenic stages are still unknown. Here, we analyzed the effects of ARA and DHA on neurogenesis, specifically maintenance and differentiation, using neurosphere assays. We confirmed that primary neurospheres are neurogenic NSPCs and that tertiary neurospheres are gliogenic NSPCs. Regarding the effects of ARA and DHA on neurogenic NSPCs, ARA and DHA increased the number of neurospheres, whereas neither ARA nor DHA had a detectable effect on NSPCs in the differentiation condition. In gliogenic NSPCs, DHA increased the number of neurospheres, whereas ARA had no such effect. In contrast, ARA increased the number of astrocytes, whereas DHA increased the number of neurons in the differentiation condition. These results suggest that ARA promotes the maintenance of neurogenic NSPCs and might induce the glial differentiation of gliogenic NSPCs and that DHA promotes the maintenance of both neurogenic and gliogenic NSPCs and might lead to the neuronal differentiation of gliogenic NSPCs.