Meditation training is proposed to enhance mental well-being by modulating neural activity, particularly alpha and theta brain oscillations, and autonomic activity. Although such enhancement also depends on the quality of meditation, little is known about how these neural and physiological changes relate to meditation quality. One model characterizes meditation quality as five increasing levels of 'depth': hindrances, relaxation, concentration, transpersonal qualities and nonduality. We investigated the neural oscillatory (theta, alpha, beta and gamma) and physiological (respiration rate, heart rate and heart rate variability) correlates of the self-reported meditation depth in long-term meditators (LTMs) and meditation-naïve controls (CTLs). To determine the neural and physiological correlates of meditation depth, we modelled the change in the slope of the relationship between self-reported experiential degree at each of the five depth levels and the multiple neural and physiological measures. CTLs reported experiencing more 'hindrances' than LTMs, while LTMs reported more 'transpersonal qualities' and 'nonduality' compared to CTLs, confirming the experiential manipulation of meditation depth. We found that in both groups, theta (4-6 Hz) and alpha (7-13 Hz) oscillations were related to meditation depth in a precisely opposite manner. The theta amplitude positively correlated with 'hindrances' and increasingly negatively correlated with increasing meditation depth levels. Alpha amplitude negatively correlated with 'hindrances' and increasingly positively with increasing depth levels. The increase in the inverse association between theta and meditation depth occurred over different scalp locations in the two groups - frontal midline in LTMs and frontal lateral in CTLs - possibly reflecting the downregulation of two different aspects of executive processing - monitoring and attention regulation, respectively - during deep meditation. These results suggest a functional dissociation of the two classical neural signatures of meditation training, namely, alpha and theta oscillations. Moreover, while essential for overcoming 'hindrances', executive neural processing appears to be downregulated during deeper meditation experiences.