London penetration depth of superconductors having lifetime broadened density of states

London penetration depth λL was calculated for superconductors having lifetime broadened density of states. With the increase of gap states, λL increases and the temperature dependence deviates from the ordinary form. The model gives a T2 dependence of λL in the case of weak-coupling limit of the Bardeen–Cooper–Schrieffer theory. The results are discussed referring to some experimental results of magnetic field penetration depth of oxide superconductors.