Two special Finsler spaces have been introduced and investigated, namely R^h-recurrent Finsler space and concircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: (i) a concircularly flat Finsler manifold is necessarily of constant curvature (Theorem A); (ii) every R^h-recurrent Finsler manifold is concircularly recurrent with the same recurrence form (Theorem B); (iii) every horizontally integrable concircularly recurrent Finsler manifold is R^h-recurrent with the same recurrence form (Theorem C).