The classic model of the respiratory system (RS) is comprised of a Newtonian resistor in series with a capacitor and a viscoelastic unit including a resistor and a capacitor. The flow interruption technique has often been used to study the viscoelastic behavior under constant inspiratory flow rate. To study the viscoelastic behavior of the RS during complete respiratory cycles and to quantify viscoelastic resistance (Rve) and compliance (Cve) under unrestrained conditions, we developed an iterative technique based on a differential equation. We, as others, assumed Rve and Cve to be constant, which concords with volume and flow dependency of model behavior. During inspiration Newtonian resistance (R) was independent of flow and volume. During expiration R increased. Static elastic recoil showed no significant hysteresis. The viscoelastic behavior of the RS was in accordance with the model. The magnitude of Rve was 3.7 +/- 0.7 cmH2O.l-1 x s, i.e., two times R. Cve was 0.23 +/- 0.051 l/cmH2O, i.e., four times static compliance. The viscoelastic time constant, i.e., Cve.Rve, was 0.82 +/- 0.11s. The work dissipated against the viscoelastic system was 0.62 +/- 0.13 cmH2O x 1 for a breath of 0.56 liter, corresponding to 32% of the total energy loss within the RS. Viscoelastic recoil contributed as a driving force during the initial part of expiration.