A brief review is given of an adaptation of the coadjoint orbit method
appropriate for the study of models with infinite-dimensional symmetr
y groups. It is illustrated on several examples, including derivation
of the WZNW action of induced D = 2 (N, 0) supergravity. As the main a
pplication, we present the geometric action on a generic coadjoint orb
it of the deformed group of area-preserving diffeomorphisms. This acti
on is precisely the anomalous effective WZNW action of D = 2 matter fi
elds coupled to a chiral W(infinity) gravity background. Similar actio
ns are given which produce the KP hierarchy as on-shell equations of m
otion.