This paper examines anomalies that arise in the transport properties of a disordered solid. The anomalies are associated with the period-r>or=2 marginally stable cycles of a keyphase recurrence relation. Their presence is signalled by divergences in standard nondegenerate perturbation theory. A 'degenerate' perturbation theory is developed within which anomalies can be computed by expanding about the cycles of interest. The low-order anomalies at energies corresponding to r=2 and 3 are evaluated and a possible extension to a system with an incommensurate potential is discussed.