This paper deals with the rate of convergence of four methods of feasible directions the Zoutendijk procedures 1 and 2 and two modifications of these procedures due to the authors. It is shown that of these methods, the two due to the authors converge linearly under convexity assumptions, that the Zoutendijk procedure 2 converges sublinearly under these assumptions, and that the Zoutendijk procedure 1 converges linearly provided the solution of the problem is a vertex of the constraint set.