A new concept of non-rapid eye movement (NREM) and rapid eye movement (REM) sleep is proposed, that of multi-component integrative states that define stable and unstable sleep, respectively, NREMS, NREMUS REMS, and REMUS. Three complementary data sets are used: obstructive sleep apnea (20), healthy subjects (11), and high loop gain sleep apnea (50). We use polysomnography (PSG) with beat-to-beat blood pressure monitoring, and electrocardiogram (ECG)-derived cardiopulmonary coupling (CPC) analysis to demonstrate a bimodal, rather than graded, characteristic of NREM sleep. Stable NREM (NREMS) is characterized by high probability of occurrence of the <1 Hz slow oscillation, high delta power, stable breathing, blood pressure dipping, strong sinus arrhythmia and vagal dominance, and high frequency CPC. Conversely, unstable NREM (NREMUS) has the opposite features: a fragmented and discontinuous <1 Hz slow oscillation, non-dipping of blood pressure, unstable respiration, cyclic variation in heart rate, and low frequency CPC. The dimension of NREM stability raises the possibility of a comprehensive integrated multicomponent network model of NREM sleep which captures sleep onset (e.g., ventrolateral preoptic area-based sleep switch) processes, synaptic homeostatic delta power kinetics, and the interaction of global and local sleep processes as reflected in the spatiotemporal evolution of cortical “UP” and “DOWN” states, while incorporating the complex dynamics of autonomic-respiratory-hemodynamic systems during sleep. Bimodality of REM sleep is harder to discern in health. However, individuals with combined obstructive and central sleep apnea allows ready recognition of REMS and REMUS (stable and unstable REM sleep, respectively), especially when there is a discordance of respiratory patterns in relation to conventional stage of sleep.