We study the magnetic field dependence of the dielectric response of large
cylindrical molecules such as nanotubes. When a field-induced level crossin
g takes place, an applied electric field has two effects: it may cause a. l
inear instead of the usual quadratic Stark effect or the difference in the
quadratic Stark coefficient of the two levels leads to a discontinuity in t
he polarization. Explicit calculations are performed for doped nanotubes an
d a rich structure in the real part of the low-frequency dielectric functio
n epsilon'(H) is found when a magnetic field is applied along the cylinder
axis. It is suggested that studies of epsilon'(H, T) can serve as a spectro
scopic tool for the investigation of large ring-shaped or cylindrical molec
ules.