  We study the geometric phase (GP)in presence of diabolic (DP) and exceptional
(EP) points. While the GP associated with the DP is the flux of the Dirac
monopole, the GP related to the EP, being complex one, is described by the flux
of complex magnetic monopole. For open systems, in week-coupling limit, the
leading environment-induced contribution to the real part of complex GP is
given by a quadrupole term, and to its imaginary part by a dipolelike field. We
find that the GP has a finite gap at the DP and infinite one at the EP.
