Earlier solutions of the problem of laminar film condensation on a horizontal tube with variable surface temperature have assumed locally radial conduction across the condensate film. The present paper describes an investigation of the effects of two-dimensional conduction, inevitably present when the surface temperature of the tube is non-uniform. It was found that the simple approach is conservative and only significantly in error for (mu k(Delta T)over bar>)/rho<(rho)over tilde>gd(3)h(fg))(1/4)greater than or equal to about 0.01, i.e. around the highest value which might be found in practice of the dimensionless parameter. When the streamwise convection term is included in the energy equation for the condensate film, the results depend (very weakly) on the additional parameter rho<(rho)over tilde>gd(3)c(p)/mu k, but are negligibly affected in the practical range.