The steady solution for the flow in the D” layer given by Stacey and Loper (1983) is generalized and placed on a firmer mathematical foundation. The stability of this flow is then analyzed and a stability criterion is developed. It is found that the stability of the flow is consistent with a lower-mantle viscosity of 0.5–1.0 1023Pas and a temperature jump of 700–800K across the layer, but if the viscosity is only 3–5 1021Pas, stability of the flow requires a much lower temperature jump. If the higher value of viscosity is correct and the flow is believed to be close to marginally stable, this argues against a second thermal boundary layer occurring elsewhere in the mantle.