Lung tissue is viscoelastic because it dissipates energy, in addition to storing energy, when stretched. This gives rise to the phenomenon of stress adaptation and creep and makes lung resistance and elastance depend on the frequency of volume cycling. Viscoelasticity is predicted in general terms by simple lumped-parameter models such as the Maxell and Kelvin bodies governed by ordinary differential equations. Lung tissue viscoelasticity is more accurately predicted by the constant-phase model, which is governed by a differential equation of fractional order. The constant-phase model predicts that stress relaxation following a step increase in strain will conform to a power-law function of time, as is observed experimentally. The combination of tissue viscoelasticity and nonlinear quasi-static stress-strain behavior observed in lung tissue can be accurately represented by quasi-linear viscoelasticity in which stress results from strain first being transformed by a static nonlinear function followed by a linear dynamic system. Although the origin of the power law stress adaptation is not fully understood, quasi-linear viscoelasticity can potentially be explained as arising from a sequence of micro-yield events that take place over time as local tissue regions of high stress break apart and pass the stress they were bearing on to other regions.