Regioselective cyclocondensation of glycine hydroxamic and dl-alanine hydroxamic acids with 1-methylpiperidin-4-one gave 1-hydroxy-8-methyl-1,4,8-triazaspiro[4.5]decan-2-one (5) and (±)-1-hydroxy-3,8-dimethyl-1,4,8-triazaspiro[4.5]decan-2-one (6), respectively. The X-ray diffraction data showed that acid 6 formed racemic crystals with two independent molecules, whose structure was studied and compared with the analog obtained earlier. The in vivo tests on the leukemia P388 and L1210 models showed that the low-toxic spirocyclic hydroxamic acids 5 and 6 were the adjuvants of clinic cytostatics cisplatin and cyclophosphamide. Chemotherapy of the leukemias P388 and L1210 was more efficient with the combination of acid 6 with cisplatin and cyclophosphamide, respectively.