The author discusses a number of controversial aspects of the search activity concept. This concept, based on an analysis of data cited by other researchers and the results of the author's own investigation, performed together with V. V. Arshavsky, postulates that search activity raises the body's resistance to stress and experimentally induced pathology whereas renunciation of search forms a nonspecific predisposition to somatic disturbances (e.g., psychosomatic disease). REM sleep is regarded as a specific form of search activity aimed at compensating for the state of renunciation of search in walking. In this paper the author argues that 1) renunciation of search can be accompanied either by anxiety or by depression, 2) REM sleep deprivation on a "small platform" raises the requirement in REM sleep by producing renunciation of search, 3) during search activity brain catecholamine synthesis is stimulated by catabolism whereas a state of renunciation of search upsets this feedback system. The actuation of the brain mechanisms of search in REM sleep necessitates a certain brain catecholamine level. If the brain catecholamine level is very high during waking behavior due to intensive search activity, the REM sleep requirement is low, REM sleep becoming reduced. After a moderate drop in the brain catecholamine level at the initial stage of renunciation of search the requirement in REM sleep rises and this phase grows longer. But at the late stage of renunciation of search the brain catecholamine level drops extremely, REM sleep shrinking in spite of the great appropriate requirement, and 4) the functional insufficiency of REM sleep invites various forms of pathology.