Phase diagrams of some globular proteins have a fluid-fluid transition as well as a fluid-crystal transition. Homogeneous nucleation of the crystal from the fluid phase near the critical point of the fluid-fluid transition is examined. As the fluid-fluid critical point is approached, the number of molecules in the critical nucleus, the nucleus at the top of the free energy barrier to nucleation, is found to diverge as the isothermal compressibility. This divergence is due to a layer of the fluid phase of width equal to the fluid's correlation length which surrounds the core of the nucleus; the number of molecules in a crystalline environment in the nucleus does not diverge. The free energy barrier to nucleation remains finite but its derivative with respect to the chemical potential is equal to minus the number of molecules in the critical nucleus, and so diverges. (C) 2001 American Institute of Physics.