The rho-axis system and the rho-axis-system Hamiltonian were devised and formulated to describe the rotational-internal-rotational motion of molecules possessing certain local geometrical symmetries. Nevertheless, they were employed to molecules without the required symmetries and apparently lying outside the range of their applicability. To justify such applications and to facilitate first-principles calculation of the corresponding spectroscopic parameters, the rho-axis-system and the rho-axis system Hamiltonian must be derived without assuming or imposing symmetry constraints. A derivation satisfying this requirement is described, and the rho-axis method is extended to molecules having a large amplitude internal motion of any kind. (C) 2003 American Institute of Physics.