  We analyse the anomalous properties of specific electronic states in the
Kronig-Penney model with weak compositional and structural disorder. Using the
Hamiltonian map approach, we show that the localisation length of the
electronic states exhibits a resonant effect close to the band centre and
anomalous scaling at the band edges. These anomalies are akin to the
corresponding ones found in the Anderson model with diagonal disorder. We also
discuss how specific cross-correlations between compositional and structural
disorder can generate an anomalously localised state near the middle of the
energy band. The tails of this state decay with the same stretched-exponential
law which characterises the band-centre state in the Anderson model with purely
off-diagonal disorder.
