  We consider slant normal magnetic curves in $(2n+1)$-dimensional
$S$-manifolds. We prove that $\gamma $ is a slant normal magnetic curve in an
$% S $-manifold $(M^{2m+s},\varphi ,\xi _{\alpha },\eta ^{\alpha },g)$ if and
only if it belongs to a list of slant $\varphi $-curves satisfying some special
curvature equations. This list consists of some specific geodesics, slant
circles, Legendre and slant helices of order $3$. We construct slant normal
magnetic curves in $\mathbb{R}^{2n+s}(-3s)$ and give the parametric equations
of these curves.
