Introduction. In this paper we present a variational method for functions of bounded boundary rotation and solve certain general extremal problems for these functions. The variational method is based upon a general method of G. M. Goluzin [1], and has previously been used by the present author to solve extremal problems for several classes of univalent functions ([7] and [8]). Once the variation formulas are derived, the details of solving the extremal problems are very similar to those in [7] and [8]. Theorem 1 here has been obtained independently by Professor J. Pfaltzgraff, who used essentially the same methods. I wish to thank Professor Pfaltzgraff for providing me with his unpublished work. Those functions of bounded boundary rotation which are also univalent form a subclass which has recently been studied by M. M. Schiffer and 0. Tammi [9]. They use a different (though closely related) variational method. We shall compare their results with ours.