We present a theoretical analysis of a model nucleation process where an oil phase separates out from a droplet microemulsion phase. We consider a homogeneous nucleation where aggregate growth occurs through addition of monomers. The nucleus is formed by the growth of an already existing microemulsion droplet. On the basis of previous equilibrium studies of the microemulsions of the same system we can be confident about the accuracy of the description of free energy changes during nucleation. Using the constraints of constant hydrocarbon volume and aggregate area, the change in curvature free energy is determined as an oil drop is nucleated rather than the change in surface free energy, as in a conventional nucleation theory. We obtain a simple analytical expression for the barrier which has the feature that it only exists in a finite parameter range. In the particular system that we have studied experimentally a two-phase system of microemulsion plus excess oil is reached through a temperature quench and a nucleation barrier is found for moderately deep quenches only. Having established an expression for the nucleation barrier, we analyze the kinetics and derive a diffusion equation in aggregate space, which considerably facilitates the calculation of the steady state rate for the formation of nuclei. Experiments confirm the existence of a nucleation barrier in the predicted range. They also show the concentration independence of the barrier and that experiments with different initial radii can be put on a common scale, as predicted. It is concluded that the system is very promising for fundamental studies of the dynamics of nucleation processes in liquids.