B.Y. Chen initiated the study of the tensor product immersion of two immersions of a given Riemannian manifold (see ). Inspired by Chen's definition, F. Decruyenaere, F. Dillen, L. Verstraelen and L. Vrancken (in ) studied the tensor product of two immersions of, in general, different manifolds; under certain conditions, this realizes an immersion of the product manifold. In  tensor product surfaces of Euclidean plane curves were investigated. In the present paper, we deal with tensor product surfaces of a Euclidean space curve and a Euclidean plane curve. We classify the minimal, totally real and slant such surfaces, respectively. © 2001 Heldermann Verlag.