The study of migration of ligands in heme proteins is one of the methods used to obtain information about the dynamics and function of biomolecules. An appropriate description of the kineticsqnvolves the modeling of transport over a series of sequential barriers. Utilizing random walk theory, the physics of ligand migration enters the modeling of the kinetics on several levels of description: By use of generalized Brownian motion theory, we develop models for biomolecular rates in presence of a frequency-dependent damping of the ligand motion. The results have the form of a modified Kramers relation. If more than one ligand moves inside a biomolecule, nonlinear blocking effects become important. The migration kinetics can then be adequately modeled by a multivariable stochastic process with nonlinear transition probabilities. Further, we discuss the limit of validity of a description of ligand migration in terms of a set of linearly coupled deterministic rate equations.