Multilayer adsorption is calculated for a one-component vapor using ideas based on the Ono-Kondo lattice model. It is shown that this model predicts the common types of adsorption behavior : the Henry, Langmuir, and Frumkin equations as particular cases; multilayer isotherms including steps due to two-dimensional condensation; changes in the isotherm that occur when the temperature is varied from subcritical to supercritical conditions. In this paper, we investigate the adsorption isotherm as the concentration approaches saturation conditions. The analysis shows that at conditions near saturation the Gibbs adsorption has a weak divergence which can be described by either a logarithmic singularity or an exponential singularity with small exponent (less than 0.05).