We have studied the magnetization in Co₈₆Tb₁₄/Pt multilayers under fields up to 1.8 T and as at room temperature. As the do-Tb layer thickness (t_CoTb) decreases below 200 Å the saturation magnetization magnetization (M) increases, the rectangularity of the M-H loops and the coercivity (H_c ) decrease. The effective anisotropy K_eff of the multilayers was determined by a torque magnetometer. The product K_eff×t_CoTb shows a linear dependence with t_CoTb as normally found for the superlatices yielding the bulk and surface anisotropies of 10⁶ erg/cm³ and –0.2 erg/cm² , respectively. These results are explained in terms of an interfacial Co-Pt layer. K_eff and H_c are related by the equation H_c = α K_effⁿ/M with the fitting parameters α and n.