The gluon propagator of QCD 2 with N f flavors of massless quarks in the light-cone is examined in the large N f limit. It is obtained from a set of identities for the gluon vertices based on the axial anomaly. The first and second order terms of a 1/ N f expansion of the two-point gluon vertex indicate that to each order the Fourier transform of the propagator has a branch point coinciding with its pole at the Schwinger mass. In contrast with QED 2 , the gluon field has no massive component corresponding to a well-defined mass. A conjecture on the singularity structure of the full propagator us presented.