The present paper is in two sections, the first section deals with special projective recurrent tensor fields while the second section deals with special recurrent Normal projective curvature tensor of order one. In the first section we have derived the necessary and sufficient conditions which are to be satisfied in order that a M_h^i ⊕ - recurrent F_n^* will be M_kh^i ⊕ - recurrent such a condition has also been derived in an affinely connected Finsler space F_n^* and in the sequel we have also derived the conditions which are to be satisfied by the fundamental function F(x,x ̇ ) and the scalar function P(x,x ̇ ) in an affinely connected M- ⊕ - recurrent F_n^*. In the second section firstly we have derived the conditions which are to be satisfied by the Normal projective curvature tensor N_jkh^i in a Normal projective recurrent Finsler space and subsequently we have observed that if the Normal projective curvature tensor be decomposable in the form N_jkh^i = Y_j^i 〖 ψ〗_kh then the tensors Y_j^i and 〖 ψ〗_kh are recurrent of order one and in the last we have established the conditions under which a Finsler space is Normal projective recurrent