For two-point boundary value problems, where no direction of integration is distinguished, symmetric Runge-Kutta methods are of particular interest. The authors present a numerical example which shows that collocation at Gauss points gives better results than collocation at Lobatto points (although both methods are symmetric, A-stable and have the same stability function). This motivates them to look for symmetric, algebraically stable Runge-Kutta methods. They give a characterization of such methods and show that the only symmetric, algebraically stable collocation schemes are those based on Gauss points.