The ESR spectra of Co²⁺ impurities in Cd₂P₂S₆ and Cd₂P₂Se₆ are reported. The Co²⁺ ion is an S=³/₂ ion and substitutes for Cd²⁺ (S=0) ions in the Cd₂P₂X₆ crystal. The spin Hamiltonian parameters g and A were determined using an effective spin=¹/₂. For Cd₂P₂S₆, g/sub ///=4.86, A/sub ///=440 MHz, g_{perpendicular to}=4,01 and A_{perpendicular to}=346 MHz. For Cd₂P₂Se₆, g/sub ///=4.98, A/sub ///=565 MHz, g_{perpendicular to}=3.85 and A_{perpendicular to}=250 MHz. From the temperature dependence of the linewidth, the zero-field splitting, 2D, for Co²⁺ doped into Cd₂P₂S₆ is estimated to be 127 cm^-1. The individual hyperfine lines of Co²⁺ doped into Cd₂P₂Se₆ show superhyperfine structure due to ⁷⁷Se(I=¹/₂, 7.58% natural abundance). This additional splitting is consistent with some covalent bonding between the Co²⁺ and its six selenium ligands.