A sleep stage classification method has been developed which uses variables derived from the Period Analyzed EEG to discriminate seven stages of sleep with accuracies of 88-99%. Period Analysis is a method through which the vast EEG data base can be condensed to a relatively small number of highly informative values. These values are the numbers of zero-crossings per second of the signal and its first and second derivatives. Stepwise discriminant analysis was used to determine which of these variables to use, and to calculate coefficients for six classification functions, based on a learning set of visually classified EEG samples. To evaluate the performance of this method various learning and test sets from the same subject were used, obtaining agreements with the visual classifier of 96-99% on reclassifications of the night in the learning set, 9-94% on intra-night test sets, and 88-94% on test sets isolated from the learning set by a month. Stage REM was discriminated from the EEG without the use of EOG leads, along with Stages I-IV, Awake, and Artifact. These inter-night hit rates were much higher than others in the current literature, and even greater than published inter-judge or even intra-judge agreements when reclassifying the same samples -- indicating a sleep stage classification system which is both highly accurate and extremely precise.