Statistical properties of parametric motion in ensembles of Hermitian banded random matrices are studied. We analyze the distribution of level velocities and level curvatures as well as their correlation functions in the crossover regime between three universality classes. It is shown that the statistical properties of level dynamics are in general nonuniversal and strongly depend on the way in which the parametric dynamics is introduced.

DOI:https://doi.org/10.1103/PhysRevE.55.2446