We find that there exist dual eigenvectors |■,q>_* of the phase state-vectors|■,q> of the two-mode Susskind-Glogower phase operator e^i?. By contour integration we show that |■,q>_* is the common eigenvector of e^－i? and the photon number difference operator. The properties of |■,q>_* are studied,it turns out that |■,q>_*and|■,q> can compose a completeness relation in contour integration form. A phase state representation for two-mode field is thus presented.