  We consider a class of conformal models describing closed strings in axially
symmetric stationary magnetic flux tube backgrounds. These models are closed
string analogs of the Landau model of a particle in a magnetic field or the
model of an open string in a constant magnetic field. They are interesting
examples of solvable unitary conformal string theories with non-trivial
4-dimensional curved space-time interpretation. In particular, their quantum
Hamiltonian can be expressed in terms of free fields and the physical spectrum
and string partition function can be explicitly determined. In addition to the
presence of tachyonic instabilities and existence of critical values of
magnetic field the closed string spectrum exhibits also some novel features
which were absent in the open string case. (Contribution to the Proceedings of
"Strings 95" Conference)
