The spreading of a liquid microdrop across a solid surface is examined using the interface formation model. This model allows for variable surface tension at constant temperature and a flow induced Maragom effect, by incorporating irreversible thermodynamics into the continuum model. The model is solved for small Capillary number and small Reynolds number. This problem has been considered before for much larger drops in Shikhmurzaev (Phys Fluids 9:266, 1997a), which examined the spreading of a drop for epsilon = tau U-CL/R << 1, where U-CL is the speed of the moving contact line across the solid surface, tau is the surface tension relaxation time of the viscous liquid, and R is a typical length scale for the size of the drop. This paper extends that work by examining epsilon = O(1), which will be shown to be the appropriate scaling for very small liquid drops, on the scale of micrometres or less.