Analytical equations for the radial drainage of uniform thin viscous films are obtained in terms of the variation in surface velocities and velocity gradients with position and time. These allow the effect of circulation in the adjacent phases and radial surface or interfacial tension gradients to be allowed for. The resultant coalescence time t(c) may be estimated from the equation t(c) = 3pimun2r(f)4/16fh(c)2, where n is given by 4/n2 = 1 + (3mur(d)/mu(d)h(i)[1 + (pir(f)3/2fh(i))(partial derivative sigma/partial derivative r)n] for a drop of radius rd approaching its homophase. Good agreement with available experimental values is obtained for drops resting at a stationary interface or moving along an inclined film.