Determination of flicker-fusion thresholds, or critical flicker frequency (CFF), by means of the generally utilized method of just noticeable differences, involves a number of practical difficulties. In the hope of overcoming these difficulties, an adaptation of the psychophysical method of constant stimuli was developed and applied to the determination of CFF. With this method, the subject is given a series of discrete exposures of the light stimulus at various constant frequencies in the neighborhood of his threshold, and he is asked to judge in each case whether or not the light is flickering. The manner in which appropriate series of stimuli are set up and applied for individual subjects, as well as the computation of the threshold and its variability by means of Spearman's arithmetic method are described in the paper. CFF determinations for 12 subjects on two successive days with both the constant stimuli and just noticeable difference method permitted a comparison of the two methods. The constant method yielded CFF values which were generally higher and more reliable than the jnd method. At the same time, the constant method resulted in greater differentiation among individuals and lower intra-individual variability. However, the two methods yielded measures which were highly correlated, especially on the second day of testing. It is concluded that the constant method described is superior to the just noticeable difference method, particularly with subjects not capable of sustained attention and difficult perceptual judgments.