Competition between magnetism and superconductivity was investigated for the newly discovered RNi(2)B(2)C superconductors with the magnetic race earth elements R=Tm, Er, Ho, Dy, and Tb. Superconductivity is also observed for the compounds with magnetic R ions and their T-c's are approximately scaled by the de Gennes factor, which implies a very weak coupling between the rare earth magnetic moments and the conduction electrons due to a small conduction electron density at the rare earth site. Associated with the antiferromagnetic order of the rare earth moments, characteristic resistive transition under magnetic field was observed.