Let us consider a symmetric linear connection and \(F\), a tensor field of \((1,1)\)-type on a manifold \(A_n\). An infinitesimal transformation of \(A_n\) is called \(F\)-\textit{planar} it it maps \(F\)-planar curves onto curves which are \(F\)-planar in their principal parts. The present paper is devoted to a study of these transformations considered as a generalization of infinitesimal geodesic transformations.