A linear model with cabbeling dynamics is developed for a nonrotating, unstratified ocean and applied to observations of three medium- to large-scale oceanic thermohaline (density balanced) fronts. The ability of the predicted cabbeling sinking and surface convergence rates to maintain a steady front against diffusion depends critically on the assumed values of horizontal and vertical eddy viscosities. There is good theoretical evidence for the existence of small-scale (1 km), weak (surface currents 0.1 cm s-1) cabbeling fronts; however, the intensity and stability of such fronts will depend critically on the scale dependent behavior of dissipation processes.