In the present paper we define a geodesic mapping of two nonsymmetrical affine connexion spaces and obtain necessary and sufficient conditions that a mapping of two such spaces be geodesic (\S 1). Particularly we study a geodesic mapping of two generalized Riemannian spaces (\S 2). Finally, we generalize the notion of Thomas's projective parameters as an invariant of geodesic mappings (\S 3).