In a previous paper there had been given a general method of investigating the motions of elastic systems, when the redressing tendencies are proportional to the extents of the disturbance. The present paper contains the results of the application of this method to the oscillations of flexible pendulums, composed of weights attached by their centres of gravity to a thread. These results, though strictly applicable only to oscillations of infinitely small extent, may yet be held as indicating the general characters of oscillations of moderate dimensions.