The voltage across the cell membrane of human T-lymphocyte cell lines was recorded by the whole cell patch clamp technique. We studied how this voltage fluctuated in time and found that these fluctuations have fractal characteristics. We used the Hurst rescaled range analysis and the power spectrum of the increments of the voltage (sampled at 0.01-sec intervals) to characterize the time correlations in these voltage fluctuations. Although there was great variability in the shape of these fluctuations from different cells, they all could be represented by the same fractal form. This form displayed two different regimes. At short lags, the Hurst exponentH=0.76±0.05 (SD) and, at long lags,H=0.26±0.04 (SD). This finding indicated that, over short time intervals, the correlations were persistent (H>0.5), that is, increases in the membrane voltage were more likely to be followed by additional increases. However, over long time intervals, the correlations were antipersistent (H<0.5), that is, increases in the membrane voltage were more likely to be followed by voltage decreases. Within each time regime, the increments in the fluctuations had characteristics that were consistent with those of fractional Gaussian noise (fGn), and the membrane voltage as a function of time had characteristics that were consistent with those of fractional Brownian motion (fBm).