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The pathophysiological aspects of parasympathetic nerve (PN) function during sleep in patients with morbid apneas/hypopneas studied by classical methods, including power-spectrum and/or time-domain analysis on heart rate variability (HRV), are highly controversial. This controversy is attributed to methodological problems such as poor time resolution in classical methods. In the present review, we describe a reliable method for investigating the PN function in patients with apneas/hypopneas, which has recently been elaborated and named “instantaneous time-frequency analysis (ITF)”. The ITF was established based on the complex demodulation (CD) algorism, which enables us to measure the transitional change in amplitude of a target frequency domain in a practically continuous manner. Among high frequency (HF) domains between 0.15 and 0.40 Hz contained in R-R intervals of electrocardiogram tracing (representative of HRV), the HF domain with the maximum amplitude was used as an approximate measure of PN activity. Based on density-spectrum-array map for main HF peak constructed with time scale of 1 sec and frequency resolution of 0.002 Hz (HF-DSA map), shift in central frequency of main HF peak over time was continuously monitored. When the main HF peak with the same central frequency lasted for more than 20 seconds or 5 minutes on HF-DSA map, the PN function was assumed “stable” or “very stable”, respectively. Based on the ITF, we elucidated the qualitative and quantitative abnormalities in PN function in patients with obstructive sleep apnea (OSA), while it was not possible to evaluate PN abnormalities in patients with central sleep apnea (CSA). Furthermore, we certified the effects of various confounding factors on PN function in OSA patients, i.e., PN activity was inhibited by aging and obesity, while PN stability was distorted by apneas/hypopneas. To establish the clinical importance of ITF, we also determined normal reference values regarding the activity and stability of PN function.