  We show that the adiabatic approximation for nonselfadjoint hamiltonians
seems to induce two non-equal expressions for the geometric phase. The first
one is related to the spectral projector involved in the adiabatic theorem, the
other one is the adiabatic limit of the nonadiabatic geometric phase. This
apparent inconsistency is resolved by observing that the difference between the
two expressions is compensated by a small deviation in the dynamical phases.
