For a respiratory system with constant compliance and resistance a constant flow can occur during part or all of inspiration in two situations: when the flow is constrained to be constant throughout inspiration, such as is the case with some mechanical ventilators, and when the applied pressure is a ramp (i.e., increasing constantly with time), which may occur during mechanical ventilation and spontaneous breathing. After initial transients in pressure and flow, respectively, have decayed away both situations result in linear volume-time and pressure-time relationships. The slope of the corresponding pressure-volume line then yields an estimate of the total compliance of the respiratory system, and the intercept, divided by the constant flow, provides the total resistance. We have shown theoretically that, for a model composed of two compartments in parallel, the total compliance is the same as the static compliance and equals the sum of the compliances of the two compartments. Furthermore, this compliance is independent of the breathing frequency. However, the total resistance is, in general, a function of both the resistances and the compliances. When the time constants of the two compartments are equal the total resistance assumes its minimum value and becomes independent of the compliances. This minimum value of resistance can be obtained, regardless of the time constants, by dividing the immediate drop in airway opening pressure, obtained after occluding during steady state inspiration, by the inspiratory flow.