Certain two-dimensional, laminar bounday layers are considered whose streamlines are closed. The speed at the solid boundary is supposed uniform, the bounday outline being stationary, and the speed in the boundary layer is supposed to differ only slightly from that of the boundary. A formal solution is then obtained for the motion in the boundary layer. The analysis confirms that a closed boundary layer may exist and yields a condition needed to determine the inviscid motion. The condition is extracted in a simplified but approximate form and two examples of its use are given. A further class of closed boundary layers, namely those for which the pressure is uniform, is also considered. For this class the condition needed to determine the inviscid motion may be derived in a form both simple and exact.