[en] The Co-sublattice anisotropy in Lu₂Co₁₇ consists of four competitive contributions from Co atoms at crystallographically different sites in the Th₂Ni₁₇-type of crystal structure, which result in the appearance of a spontaneous spin-reorientation transition (SRT) from the easy plane to the easy axis at elevated temperatures. In order to investigate this SRT in detail and to study the influence of Si substitution for Co on the magnetic anisotropy, magnetization measurements were performed on single crystals of Lu₂Co_17-xSi_x (x=0-3.4) grown by the Czochralski method. The SRT in Lu₂Co₁₇ was found to consist of two second-order spin reorientations, 'easy-plane'-'easy-cone' at T_SR1∼680 K and 'easy-cone'-'easy-axis' at T_SR2∼730 K. Upon Si substitution for Co, both SRTs shift toward the lower temperatures in Lu₂Co₁₆Si (T_SR1∼75 K and T_SR2∼130 K) with the further onset of the uniaxial type of magnetic anisotropy in the whole range of magnetic ordering for Lu₂Co_17-xSi_x compounds with x>1 due to a weakening of the easy-plane contribution from the Co atoms at the 6g and 12k sites to the total anisotropy