Neutron diffraction and thermodynamics techniques were used to probe the evolution of the magnetic properties of Tb(Co_{x}Ni_{1-x})_{2}B_{2}C. A succession of magnetic modes was observed as x is varied: the longitudinal modulated k=(0.55,0,0) state at x=0 is transformed into a collinear k=([nicefrac]<LaTeX> icefrac{1}{2}</LaTeX>,0,[nicefrac]<LaTeX> icefrac{1}{2}</LaTeX>) antiferromagnetic state at x= 0.2, 0.4; then into a transverse c-axis modulated k=(0,0,[nicefrac]<LaTeX> icefrac{1}{3}</LaTeX>) mode at x= 0.6, and finally into a simple ferromagnetic structure at x= 0.8 and 1. Concomitantly, the low-temperature orthorhombic distortion of the tetragonal unit cell at x=0 is reduced smoothly such that for x >= 0.4 only a tetragonal unit cell is manifested. Though predicted theoretically earlier, this is the first observation of the k=(0,0,[nicefrac]<LaTeX> icefrac{1}{3}</LaTeX>) mode in borocarbides; our findings of a succession of magnetic modes upon increasing x also find support from a recently proposed theoretical model. The implication of these findings and their interpretation on the magnetic structure of the RM_{2}B_{2}C series are also discussed.
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