The arms in spiral galaxies cannot be material arms for then they would wind up on a time scale of one galactic rotation, or a few times 108 years. The large number of spirals suggests that the spiral pattern must persist for about 1010 years (or be continually rejuvenated). The density wave theory treats the spiral pattern as a wave phenomenon, thus overcoming this problem. Much work has been done studying small amplitude oscillations in flat stellar discs. Self-consistent spiral modes have been found, but they are not stable and grow at a fast rate. Numerical simulations of thin stellar discs, such as those of Hohl (1971), which can handle finite amplitude waves, have been more successful. Spiral waves form initially but evolve into a steady state rotating bar. It seems therefore, that a long-lived spiral cannot be formed in stars alone.