Unstable (cyclical alternating pattern, or CAP) sleep is associated with surges of sympathetic nervous system activity, increased blood pressure and vasoconstriction, heightened baroreflex sensitivity, and unstable heart rhythm and breathing. In susceptible persons, CAP sleep provokes clinically significant events, including hypertensive crises, sleep-disordered breathing, and cardiac arrhythmias. Here we explore the neurophysiology of CAP sleep and its impact on cardiovascular and respiratory functions. We show that: (i) an increase in neurophysiological recovery rate can explain the emergence of slow, self-sustained, hypersynchronized A1 CAP-sleep pattern and its transition to the faster A2-A3 CAP-sleep patterns; (ii) in a two-dimensional, continuous model of cardiac tissue with heterogeneous action potential duration (APD) distribution, heart rate accelerations during CAP sleep may encounter incompletely recovered electrical excitability in cell clusters with longer APD. If the interaction between short cycle length and incomplete, spatially heterogeneous repolarization persists over multiple cycles, irregularities and asymmetry of depolarization front may accumulate and ultimately lead to a conduction block, retrograde conduction, breakup of activation waves, reentrant activity, and arrhythmias; and (iii) these modeling results are consistent with the nighttime data obtained from patients with structural heart disease (N=13) that show clusters of atrial and ventricular premature beats occurring during the periods of unstable heart rhythm and respiration that accompany CAP sleep. In these patients, CAP sleep is also accompanied by delayed adaptation of QT intervals and T-wave alternans.