  Level crossing models for two-state quantum systems are applicable to a wide
variety of physical problems. We address the special case of level glancing,
i.e., when energy levels reach a degeneracy at a specific point of time, but
never actually cross. The simplest model with such behaviour is the parabolic
model, and its generalizations, which we call superparabolic models. We discuss
their basic characteristics, complementing the previous work on the related
nonlinear crossing models [Phys. Rev. A 59, 4580 (1999)].
