Time-domain estimation has been invoked for tracking of respiratory mechanical properties using primarily a simple single-compartment model containing a series resistance (Rrs) and elastance (Ers). However, owing to the viscoelastic properties of respiratory tissues, Rrs and Ers exhibit frequency dependence below 2 Hz. The goal of this study was to investigate the bias and statistical accuracy of various time-domain approaches with respect to model properties, as well as the estimated impedance spectra. Particular emphasis was placed on establishing the tracking capability using a standard step ventilation. A simulation study compared continuous-time versus discrete-time approaches for both the single-compartment and two-compartment models. Data were acquired in four healthy humans and two dogs before and after induced severe pulmonary edema while applying sinusoidal and standard ventilator forcing. Rrs and Ers were estimated either by the standard Fast Fourier Transform (FFT) approach or by a time-domain least square estimation. Results show that the continuous-time model form produced the least bias and smallest parameter uncertainty for a single-compartment analysis and is quite amenable for reliable on-line tracking. The discrete-time approach exhibits large uncertainty and bias, particularly with increasing noise in the flow data. In humans, the time-domain approach produced smooth estimates of Rrs and Ers spectra, but they were statistically unreliable at the lower frequencies. In dogs, both the FFT and time-domain analysis produced reliable and stable estimates for Rrs or Ers spectra for frequencies out to 2 Hz in all conditions. Nevertheless, obtaining stable on-line parameter estimates for the two-compartment viscoelastic models remained difficult. We conclude that time-domain analysis of respiratory mechanics should invoke a continuous-time model form.