Trains of nerve impulses from the crayfish stretch receptor under steady conditions are found to be extremely regular with a standard deviation of S = 0.7 x 10(-2)tau when tau, the mean interval, is in the 15 to 80 msec range. Such a small fluctuation increases the problems of film recording, accurate measurement of intervals, and especially, drifts. Experimental and mathematical techniques are described to obviate these problems. Evidence is found for a serial correlation coefficient of about -0.2 in the range, tau = 35 msec to tau = 70 msec. Shot noise and Johnson noise in a long axon are evaluated in detail and are shown to be comparable in size. It is also shown that neither shot noise nor Johnson noise is large enough to explain simply the observed interval fluctuations. Other types of membrane noise are discussed.