  We theoretically study the orbital magnetic susceptibility produced by
electron states near a crossing point of two band-contact lines in a crystal.
It is shown that this susceptibility can have an unusual dependence on the
Fermi level and can change noticeably with the temperature when the Fermi level
is in the vicinity of the crossing point. These features of the magnetic
susceptibility can be useful in detecting the crossing points in crystal. The
obtained results explain the well-known temperature dependence of the magnetic
susceptibility of V$_3$Si.

Mesoscale and Nanoscale Physics