I. Bars We investigate regular and chaotic two-dimensional (2D) and three-dimensional (3D) orbits of stars in models of a galactic potential consisting of a disk, a halo, and a bar to find the origin of boxy components that are part of the bar or (almost) the bar itself. Our models originate in snapshots of an N-body simulation, which develops a strong bar. We consider three snapshots of the simulation, and, for the orbital study, we treat each snapshot independently, as an autonomous Hamiltonian system. The calculated corotation−to−bar length ratios indicate that in all three cases, the bar rotates slowly, while the orientation of the orbits of the main family of periodic orbits changes along its characteristic. We characterize the orbits as regular, sticky, or chaotic after integrating them for a 10 Gyr period by using the GALI₂ index. Boxiness in the equatorial plane is associated either with quasi-periodic orbits in the outer parts of stability islands or with sticky orbits around them, which can be found in a large range of energies. We indicate the location of such orbits in diagrams, which include the characteristic of the main family. They are always found about the transition region from order to chaos. By perturbing such orbits in the vertical direction, we find a class of 3D nonperiodic orbits, which have boxy projections both in their face-on and side-on views. II. Spiral Arms The PERLAS potential has been successfully used in many studies related to the dynamics of the spiral arms on the equatorial plane of normal (nonbarred) spiral galaxies. In the present work, we extend these studies by investigating the three-dimensional (3D) dynamics of the spiral arms in the same type of potential. We consider a typical open, logarithmic, spiral pattern of pitch angle 25° and we examine the stellar orbits that can support it as the ratio of the masses of the spiral over the disk component (Ms/Md) varies. We indicate the families of (3D) 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 quasiperiodic and nonperiodic orbits in general that follow spiral-supporting orbits as the Ms/Md ratio increases. We find that a bisymmetric spiral with 25° pitch angle is better supported by orbits in models with 0.03⪅ Ms/ Md ⪅ 0.07.