In order to describe molecular properties which depend on the instantaneous nuclear geometry, such as the potential energy and electric and magnetic moments, it is advantageous to use geometrically defined (i.e., mass independent) internal coordinates (bond lengths, interatomic distances, valence angles, dihedral angles). In the case of systems possessing a high degree of contortion instability, these coordinates may also be most suitable for describing the rovibrational dynamics (see [1] and references therein). The construction of the corresponding quantum mechanical Hamiltonians has been undertaken in many laboratories (see, e.g., [2–10]) and several of these studies provide theory for a general molecule. However, the use of curvilinear coordinates leads to very complicated expressions for the kinetic energy operator and for larger systems it may become prohibitively difficult to derive this operator. To avoid these problems, it is desirable to reduce the dimensionality of the studied problems by imposing model constraints (i.e., by freezing or constraining internal coordinates). However, it is not straightforward to impose such constraints even when the operator for the corresponding constraint-free task is known (see, e.g., [11,12] and references therein). It is similarly difficult to impose dynamic constraints such as Eckart and Sayvetz conditions (see, e.g., [13]) as shown by the fact that almost all curvilinear calculations were performed without such constraints; in these calculations the molecule-fixed axis system is attached directly to the instantaneous configuration of the molecule. Disregarding the dynamic constraints reduces the degree of separability of the vibrational motions from the over-all molecular rotation, thus deteriorating the quality of the vibrational zero-order models. Moreover, it also prevents an accurate determination of the vibrational observables associated with vector and tensor molecular properties (see, e.g., [14]). The curvilinear coordinates also play an important role in the framework of molecular dynamics semiclassical simulations, though these simulations are usually performed in terms of the Cartesian coordinates. For instance [15], a computer simulation of molecular liquids requires that at each simulation step the Eckart geometry be determined from the instantaneous values of the internal coordinates (in order to account for the Coriolis coupling contributions to the correlation functions). Apparently, the transformation from the internal (curvilinear) coordinates to the constrained Cartesian coordinates in the Eckart frame is of basic importance in a broad area of molecular physics. In general, this transformation leads to the solution of a system of nonlinear equations which can be derived from the imposed constraints and geometrical definitions of the internal coordinates. In principle, these equations may have nonunique solutions. However, if we eliminate large-amplitude motions from the vibrational part of a given dynamical problem, using for instance the Hougen–Bunker–Johns approach [16], we can assume that the vibrational displacements are small enough to allow for an unambiguous solution of the given problem. In the actual solution of the equations one can proceed either numerically or analytically. Though fairly general, the numerical approach [17] is inconvenient from many respects. An analytical solution of the problem in a closed form, on the other hand, appears to be available only in the case of triatomics [18–20]. However, due to the assumption of the infinitesimal character of the vibrational displacements, we may seek for solutions Journal of Molecular Spectroscopy 217 (2003) 142–145