The problem of surface-wave propagation over the modified Goubau line, which consists of a Goubau line with an airgap between the conductor and dielectric, is formulated by the boundary-value method. The various modes which exist on the line as well as their cutoff conditions and the specific effects of the airgap are obtained from a solution of the characteristic equation. The mode spectrum for the symmetric and hybrid modes as well as the transverse field distributions for the E00 and H01 modes are also presented. The axial power flow and the attenuation constant are calculated for the dominant mode and the salient low-loss feature may be explained perhaps in terms of total internal reflection or duct propagation phenomena.