We study ordered and chaotic orbits in barred galaxies. Both types of orbits are important in constructing self-consistent models. We have developed two new criteria for characterizing ordered and chaotic orbits, the stretching numbers (or short-time Lyapunov characteristic numbers) and the helicity angles (the angles between the current deviations from a given orbit and a fixed direction). The distributions of successive stretching numbers and helicity angles are the spectra of an orbit. These are invariant with respect to initial conditions in a chaotic domain. The helicity angles give the fastest method up to now for separating ordered and chaotic orbits. They are more efficient than rotation angles, which cannot always be defined. A comparison of our method with Laskar's frequency analysis method is made. In 3-D systems we define one spectrum for stretching numbers and three spectra for helicity angles. A clear distinction between Arnold diffusion and resonance overlap diffusion is made.