  We consider a unit speed curve $\alpha$ in Euclidean $n$-dimensional space
$E^n$ and denote the Frenet frame by $\{v_1,...,v_n\}$. We say that $\alpha$ is
a cylindrical helix if its tangent vector $v_1$ makes a constant angle with a
fixed direction $U$. In this work we give different characterizations of such
curves in terms of their curvatures.
