Based on the theory of spectral degree of cross-polarization, the behaviour of spectral degree of cross-polarization of a electromagnetic Gaussian Schell-model beam on propagation is studied. The expressions for the elements of the cross-spectral density matrix the beam propagating in free space for arbitrary two points in the beam has been derived by using the unified theory of coherence and polarization and the extended Heygens-Fresnel integral. The results show that, the degree of cross-polarization of partially coherent electromagnetic beams in free space may take on any nonnegative values, in contrast to the usual degree of polarization which is restricted to the range 0~1.The behavior of the degree of cross-polarization on propagation is determined by all the parameters of the source radiating the beam. At sufficiently large distances from the source the degree of cross-polarization stabilizes for all points within the beam independently of their radial positions.The condition for keeping the degree of cross-polarization invariant is the same as that of the usual degree of polarization.