  The PERLAS potential has been successfully used in many studies related with
the dynamics of the spiral arms \textit{on} the equatorial plane of normal
(non-barred) spiral galaxies. In the present work we extend these studies by
investigating the three-dimensional dynamics of the spiral arms in the same
type of potential. We consider a typical open, logarithmic, spiral pattern of
pitch angle 25$^{\circ}$ and we examine the stellar orbits that can support it
as the ratio of the masses of the spiral over the disk component
($M_{s}/M_{d}$) varies. We indicate the families of `three-dimensional'
periodic orbits that act as the backbone of the spiral structure and we discuss
their stability in the models we present. We study further the quasi-periodic
and non-periodic orbits in general that follow spiral-supporting orbits as the
$M_{s}/M_{d}$ ratio increases. We find that a bisymmetric spiral with
25$^{\circ}$ pitch angle is better supported by orbits in models with
$0.03\lessapprox M_{s}/M_{d} \lessapprox 0.07$. In these cases a strong spiral
pattern is supported between the radial 2:1 and 4:1 resonances, while local
enhancements of the imposed spirals are encountered in some models between 4:1
and corotation. A characteristic bar-like structure is observed in all models
at radii smaller than the radius of the 2:1 resonance.
