First we introduce the notion of F-algebroids, which is a generalization of F-manifold algebras and F-manifolds, and show that F-algebroids are the corresponding semiclassical limits of pre-Lie formal deformations of commutative associative algebroids.Then we use the deformation cohomology of pre-Lie algebroids to study pre-Lie infinitesimal deformations and extension of pre-Lie n-deformations to pre-Lie (n + 1)-deformations of a commutative associative algebroid.Next we develop the theory of Dubrovin's dualities of F-algebroids with eventual identities and use Nijenhuis operators on Falgebroids to construct new F-algebroids.Finally we introduce the notion of pre-F-algebroids, which is a generalization of F-manifolds with compatible flat connections.Dubrovin's dualities of pre-F-algebroids with eventual identities, Nijenhuis operators on pre-F-algebroids are discussed.