We study the buckling of a pre-stressed coated elastic half-space with the aid of the exact theory of nonlinear elasticity, treating the coating as an elastic layer and using its thickness as a small parameter. Two asymptotic limits are identiยฎed: e jilk =O(khe jilk ) and e jilk =O(k 3 h 3 e jilk ), where e jilk and e jilk are the elastic moduli for the halfspace and the coating, respectively, k is a mode number and h the thickness of coating. The ยฎrst limit corresponds to the case when the coating and half-space exert maximum eect on each other and the second limit corresponds to the classical model equation for a plate supported by an elastic foundation. For each limit the leading order bifurcation condition is derived using two dierent methods. In the ยฎrst method we derive the leading order governing equations ยฎrst and then obtain from them the bifurcation condition. In the second method we derive the exact bifurcation condition ยฎrst and then take the thin-layer limit. The two methods are found to yield the same results, assuring us that the leading order governing equations are asymptotically consistent. These leading order governing equations in the thin-layer limit are then compared with those assumed or derived by previous researchers.