The character of heat transport by cellular convection, which arises beyond the marginal state of stability in a layer of fluid bound between two constant temperature surfaces is examined. It is shown that a simple equation characterizes the heat transport in the neighborhood of the marginal state of stability when the convection is steady, and its cellular pattern of motion is represented by the solutions of the linear theory. The results of the study include all three cases of boundary conditions, namely, when the bounding surfaces of the layer are both free, are both rigid, or one is free and the other is rigid.