  Integrable perturbations of the nonholonomic Suslov, Veselova, Chaplygin and
Heisenberg problems are discussed in the framework of the classical
Bertrand-Darboux method. We study the relations between the Bertrand-Darboux
type equations, well studied in the holonomic case, with their nonholonomic
counterparts and apply the results to the construction of nonholonomic
integrable potentials from the known potentials in the holonomic case.
