In this study, rstly, new proofs of the theorems which characterize the generalized helices, slant helices and relatively-normal slant helices are presented by using the Darboux vectors of these helices. Also, a characterization of a generalized helix lying on an oriented surface is given in terms of its geodesic curvature, geodesic torsion and normal curvature. Secondly, by dening B1-slant helix in Euclidean 4-space, we give its characterization.