The electrical and structural properties of NdNiC2 and PrNiC2 are examined in single-crystalline samples in order to investigate the interplay of charge-density wave (CDW) and magnetic order in ternary rare-earth nickel carbides, RNiC2, where R is a rare-earth element. PrNiC2 (no magnetic order down to 1.5 K) and NdNiC2 [antiferromagnetic (AF) transition at 17.2 K] show resistance anomalies at 89 and 121 K, respectively, which are revealed to be CDW transitions by observing X-ray satellite reflections. NdNiC2 also shows a gradual decrease in both resistivity and CDW amplitude below the Neel temperature. In the AF phase, the magnetoresistance sharply decreases where a ferromagnetic (FM) order occurs, which is realized above the spin-flop magnetic field. These results clearly suggest that the relationships between CDW and magnetic order in RNiC2 depend on whether the magnetic order is AF or FM.