Does each spiral Galaxy house a slowly growing elliptical one?

N-body simulations performed by us suggest a mechanism for the generation of spiral waves in galaxies in which a mutual quasi-ellipsoidal rotating equilibrium configuration increasing slowly by accretion from the surrounding disk influences the density distribution of stars in the disk such as to give rise to a trailing spiral density wave. Interaction of the spiral wave with the viscous interstellar gas and mutual gravitation between the stars in the disk are believed to influence the form of the spiral. Nevertheless the basic assumption of conventional density wave theory according to which the mutual interaction of stars in the disk is essential for the formation of spirals may not be true.