An algebraic scheme for describing nonrigid polyatomic molecules is introduced and used to characterize bending motion in 'floppy' triatomic/tetratomic species. The salient features of quasi-linear and quasi-bent molecules are classified systematically. In particular, the (nu(5)) bending vibration supported by the ground electronic state of fulminic acid (HCNO/DCNO) is shown to exhibit the predicted behavior for nonrigidity. Likewise, the (nu(2)) bending motion of magnesium hydroxide (MgOH/MgOD) demonstrates quantitative application of this novel approach to problems of spectroscopic interest. Effective potential energy functions for these large-amplitude degrees of freedom are extracted by exploiting the method of coherent states. (C) 2003 Elsevier Science B.V. All rights reserved.