Extraction properties of N,N-di(2-ethylhexyl)-2,2-dimethylpropanamide (DEHDMPA) for nitric acid, U(VI), and Pu(IV) were studied by a batch method using various nitric acid concentrations. The distribution ratio equations for nitric acid, U(VI), and Pu(IV) were derived. A continuous counter-current experiment was performed using mixer-settler extractors to determine the performance of a process that uses two types of monoamides, DEHDMPA and N,N-di(2-ethylhexyl)butanamide (DEHBA), as extractants. This process consisted of two cycles: one dedicated to extraction of U(VI) by DEHDMPA, and the other dedicated to the co-extraction of U(VI) and Pu(IV) by DEHBA. The feed solution used for the continuous counter-current experiment was 4 mol/dm3 nitric acid containing U(VI), Pu(IV), and simulated fission products. DEHDMPA exclusively extracted U(VI) from the feed at the 1st cycle, and the ratio of U recovered in the U fraction stream was 99.93%. The residual U and almost all Pu were extracted by DEHBA in the 2nd cycle, and the recovery of Pu in the U-Pu fraction stream was 99.94%. Concentration profiles of U and Pu in mixer-settlers were calculated using a simulation code, which confirmed that the calculation was effective for estimating the U concentration in the U fraction stream, and the U and Pu concentrations in the U-Pu fraction stream.