We consider a thin rare-earth film with the c axis perpendicular to the sur
face, to study its nonuniform magnetic structure induced by the lower coord
ination near the surfaces. The influence of a de magnetic field, applied pe
rpendicular to the c axis, on the equilibrium configurations is also invest
igated. The spin-wave frequencies, in the q=0 limit, are calculated as a fu
nction of the strength of the external de field. We use the bulk parameters
of dysprosium and holmium to obtain the external field dependence of the e
quilibrium configuration, magnetization, and the lowest spin-wave modes of
30-monolayer-thick films. [S0163-1829(99)10209-1].