Neutron powder diffraction experiments have been carried out on the hexagonal ternary silicides Nd₆Co_1.67Si₃ and Tb₆Co_1.67Si₃ in order to determine their magnetic structures. These compounds exhibit two successive ferromagnetic transitions at <i>T</i>_C = 84 K and <i>T</i>₁ = 40 K for Nd₆Co_1.67Si₃ and at <i>T</i>_C = 186 K and <i>T</i>₁ = 171 K for Tb₆Co_1.67Si₃. Single-crystal x-ray diffraction and specific heat measurements have been realized on Tb₆Co_1.67Si₃ in order to complete its characterization. Neutron diffraction investigation at 1.5 K reveals for both compounds a canted ferromagnetic structure with a propagation vector <b><i>k</i></b> = (0 0 0). The Nd moment values are, respectively, equal to μ₁ = 2.06(10)μ_B and μ₂ = 3.14(9)μ_B for Nd1 and Nd2 atoms whereas Tb1 and Tb2 atoms carry a magnetic moment of μ₁ = 7.9(2)μ_B and μ₂ = 8.9(2)μ_B in Tb₆Co_1.67Si₃. Moreover, a transition from a canted ferromagnet to a pure ferromagnet occurs at <i>T</i>₁ = 40 K in Nd₆Co_1.67Si₃ while a spin reorientation of the non-collinear ferromagnetic structure occurs at <i>T</i>₁ = 171 K for Tb₆Co_1.67Si₃. These magnetic structures are discussed on the basis of the atomic disorder existing for Co atoms in these ternary silicides around the Nd1 and Tb1 atoms.Read less <