This paper introduces time domain methods for relating fluctuations in heart rate (HR) to respiration. Three methods: (1) linear stationary, (2) linear non-stationary and (3) non-linear approaches are described. (1) Experimental and signal processing contrivances called random breathing and noise injection methods enable the stable estimation of the impulse response of the HR to the instantaneous lung volume (ILV) signals. The comparison of the HR power spectra and the inpulse response revealed that the respiratory HR fluctuations are mostly affected by the parasympathetic autononic nervous activity. (2)Adaptive signal processing techniques enable recursive estimation of the impulse response, which allows us to keep track its temporal changes. Computer simulation confirmed the feasibility of the method in a practical situation. (3)An index called the degree of non-linearity (d.n.) has been introduced to evaluate how much non-linear the system is. Computer simulation confirmed the validity of the estimation method. Real data analysis showed that 30-35 % of the HR fluctuations associated with ILV cannot be predicted by the linear combination of ILV signals.