There are both monotonic and rhythmic factors in the patterns of change seen in physiological, psychological, and performance variables during sleep deprivation. These monotonic and rhythmic factors can be orthogonal, or they may interact with each other, with various task variables, or both. The importance of separating the rhythmic from the monotonic factors and of elucidating their interactions is discussed. Experimental methods and types of analysis appropriate to evaluating these factors are examined, with special emphasis on the complex demodulation time series analysis applied to group or individual subject data. The discussion is accompanied by data illustrations. It is suggested that sleep deprivation research should be designed so as to generate physiological and behavioral data that include information on both monotonic and rhythmic factors, the nature and extent of their interaction, and how they interrelate with systematically manipulated independent variables.