The original collective Hamiltonian is generalised to coupled multipole modes describing low-energy collective motion in nuclei. This Hamiltonian is applied to the quadrupole and octupole degrees of freedom coupled to each other. Methods for a numerical solution of the full problem are presented. The well known models of octupole excitations in spherical and strongly deformed nuclei are derived by means of the small-amplitude expansion around the equilibrium. A model of this kind is also derived for the case when a static octupole deformation occurs, which seems to be essential for nuclei in the Ra-Th region.