The geometry of the Lie algebroid generalized tangent bundle of a generalized Lie algebroid is developed. Introducing the notion of geodesic of a mechanical (rho, eta)-system with respect to a (rho, eta)-spray, the Berwald (rho, eta)-derivative operator ans its mixed curvature, we obtain main result to concetualize the Wheyl's method in this general framework. Finally, we obtain to new results of Wheyl type for the geometry of mechanical (rho, eta)--systems.
