This chapter discusses Tomonaga gas model, collective oscillation in π-electron system in aromatic hydrocarbons and collective oscillation in linear conjugated molecule. There are two methods of approach in the treatment of quantum-mechanical collective motions. Tomonaga has developed a theory of collective motion that is applicable to a large class of dynamical systems provided the system is actually capable of performing collective motions, not only longitudinal oscillation but also surface oscillations similar to that of an incompressible fluid. This theory is a natural generalization of the use of center-of-mass coordinates to describe translational motions and to separate them for the internal relative motions of the system. In the free-electron model for the pi-electrons in aromatic hydrocarbons the electrons are assumed to move freely along the circumference of a circle in a zero potential field. The pi-electrons in effect form a two-dimensional electron gas. Because of the electrostatic repulsion between the electrons, a dynamical system consisting of N electrons will strongly resist compression of the system. The electrons will move in such a way that the density undergoes no change because in this motion the change of potential energy will be smallest. The motion is most likely to occur in systemisa two-dimensional collective oscillation. It is surmised, therefore, that the quantum-mechanical collective motion proposed by Tomonaga will be applicable to the pi-electron system in aromatic hydrocarbons. © 1972, Academic Press, Inc.