Fano factor analysis and dispersional analysis were used to characterize time series of single and multifiber spikes recorded from the preganglionic cervical sympathetic nerve and cardiac-related slow-wave activity of the whole postganglionic sympathetic vertebral nerve (VN) in anesthetized cats. Fluctuations in spike counts and interspike intervals for single preganglionic fibers proved to be fractal (i.e., time-scale invariant), as reflected by a power law relationship between indices of the variance of these properties and the window size used to make the measurements. Importantly, random shuffling of the data eliminated the power law relationships. Fluctuations in spike counts in preganglionic multifiber activity also were fractal, as were fluctuations in the height and of the area of cardiac-related slow waves recorded from the whole postganglionic VN. These fractal fluctuations were persistent (i.e., positively correlated), as reflected by a Hurst exponent significantly >0.5. Although fluctuations in the interval between cardiac-related VN slow waves were random, those in the interval between heart beats were fractal and persistent. These results demonstrate for the first time that apparently random fluctuations in sympathetic nerve discharge are, in fact, dictated by a complex deterministic process that imparts "long-term" memory to the system. Whether such time-scale invariant behavior plays a role in generating the fractal component of heart rate variability remains to be determined.