A model for monomers on a lattice is presented based on local density calculations that were first proposed by Ono and Kondo in 1947 and recently generalized by Aranovich, Donohue, and co-workers. The model allows one to describe the adsorption behavior of molecules at a surface (or interface), and the phase behavior of adsorbed molecules, as well as of molecules in the bulk on the basis of short-range ordering in two and three dimensions. While there are prior lattice theories that predict nonrandom behavior for arbitrary lattice coordination numbers, the derivation of adsorption models from these theories is usually based on ideal fluid behavior in the bulk. However, the new adsorption model presented here is consistent in that molecular behavior in the bulk as well as in the adsorbed surface layer is based on identical assumptions. This is accomplished by calculating the total free energy of the system; the corresponding adsorption model follows through minimization of the free energy. This procedure is also used for deriving a new adsorption equation based on the quasi-chemical approximation to the Ising problem. Results from this equation are very similar to those obtained from the equation based on Ono-Kondo theory. When compared with lattice Monte Carlo computer simulations, the new adsorption models based on nonrandom mixing consistently show better agreement than those based on random behavior. For simplicity, the discussion of results is restricted to single-component systems. However, the new adsorption model based on Ono-Kondo theory is applicable to systems of arbitrary numbers of components without introducing any further assumptions.