Let us consider a manifold provided with a non-linear connection. In the preceding paper [6] we have defined a notion of a holonomy mapping and found a gemetrical significance for the condition that the hv-curvature tensor of a Finsler connection vanishes. In the present paper, we investigate the holonomy mappings in detail and consider, in connection with the holonomy mappings, the character of Landsberg spaces, Berwald spaces, generalized Berwald spaces and almost Hermitian Finsler spaces
