A new theoretical model is proposed for dispersive field-line resonances in collisionless magnetospheric plasmas on the basis of reduced four-field equations. The model improves upon the predictive capabilities of earlier two-field models. In particular, due to the coupling of the shear-Alfv¿n mode to the slow mode in the four-field system, it is now possible to account for the observed low frequencies of field-line resonances. Furthermore, parallel electric fields can be large without requiring the field-aligned current density to be unrealistically large. Qualitative implications for recent FAST and ground-based observations are discussed. ¿ 1999 American Geophysical Union