Separation patterns are classified into three types (regular, singular and combination types) by the property of the differential equation, the solution of which gives limiting streamlines. A criterion for the three-dimensional separation line is deduced from the negation of the Lipschitz's condition. The criterion is applied to the existing limiting streamlines over a ellipsoid of revolution at incidence, and also to the calculated ones on a ship hull. The results show that the present criterion is available for the prediction of the three-dimensional separation line.