Using three different approaches, each with different theoretical assumptions, we showed that mammalian neuronal spike trains contain serial ordering. We demonstrated that: (1) when intervals are categorized according to whether their durations are short, medium, or long, sequential groupings of adjacent interval categories exhibit Markov dependencies, extending to at least the 4th order; (2) the observed incidence of specified patterns of these groups of adjacent interval categories differs from the independent case, based on Chi square goodness-of-fit tests, and by using similar procedures; (3) there is divergence from independence when adjacent interval patterns are described in terms of relative lengths of adjacent intervals. The statistical indicators of serial dependence were significantly greater when applied to the original data than when applied to the same data after shuffling. Each of these approaches leads to the notion that "information" is carried in clusters of adjacent intervals ("bytes" or "words") and moreover, we can identify which specific patterns of interspike intervals contribute most to the statistical significance (i.e., those clusters that are potential candidates for "information carriers"). In most of the ten neurons, the "memory" of the system appears to be at least 36--45 msecs.