To determine whether renal blood flow is regulated against spontaneous fluctuations in arterial pressure and to estimate the frequency band of the regulation, we measured arterial pressure and renal blood flow continuously over several days in conscious dogs. Mean arterial blood pressure showed broad band fluctuations and behaved as a 1/f process, indicating that the blood pressure record is a fractal curve and therefore scale invariant. The fluctuations in arterial pressure caused attenuated fluctuations in renal blood flow; the gain was about -6.5 ± 0.5 dB through all sampled frequencies ≥4 cycle/day. The kidney did not attenuate the blood pressure signal at the lowest frequencies. The results show that renal blood flow is better regulated against fluctuations in pressure at frequencies ≥4 cycle/day than it is at lower frequencies. Although there are no direct tests of the underlying regulatory mechanisms, we argue that the responses are generated locally and can be identified with renal autoregulation.