The intervals between successive action potentials (impulses, or "spikes") produced the maintained firing of a neuron (ISIs) are often treated as if they were independent on each other; that is, an impulse train is considered as a stationary renewal process. If this is so, the variability of the mean rate of firing impulses in a sequence of temporal windows should be predictable from the distribution of ISIs. This was found not to be the case for the maintained firing of retinal ganglion cells in goldfish. Although some evident nonstationarity sometimes resulted in greater variability of the observed rate distributions than those predicted (for relatively long temporal windows), as a general rule the observed rate distributions were considerable less dispersed than would be predicted by sampling of the ISI distributions. This was taken as evidence of long-term serial dependency between successive ISIs; however, two standard test for dependency (autocorrelations and serial correlograms failed to to reveal structure of sufficiently long duration to account for the effect noted.