  We consider complex Fermi curves of electric and magnetic periodic fields.
These are analytic curves in C^2 that arise from the study of the eigenvalue
problem for periodic Schroedinger operators. We characterize a certain class of
these curves in the region of C^2 where at least one of the coordinates has
"large" imaginary part. The new results in this work extend previous results in
the absence of magnetic field to the case of "small" magnetic field. Our
theorems can be used to show that generically these Fermi curves belong to a
class of Riemann surfaces of infinite genus.
