Variable viscosity solutions have been obtained laking account of both radial and tangential temperature variation. Solutions have been obtained for ethylene glycol, which has a strong dependence of viscosity on temperature, and for both free and forced convection. For uniform surface temperature, constant-property solutions, with an appropriate reference temperature, give accurate results for the mean heat-transfer coefficient, even where the viscosity varies across the condensate film by a factor of around 10. Constant-property solutions are much less accurate in the presence of appreciable circumferential wall temperature variation. The theoretical results are compared with heat-transfer measurements for condensation of ethylene glycol.