To produce protein crystals with good quality is an essential process for the X-ray crystallography of protein molecules. Protein crystallization, however, depends entirely on empirical methods, which vary for each protein. We have so far suggested that the lipid cubic phases consist of nanoscopic water 'cells' provide a new environment to enhance the protein crystallization. The essential mechanism of the enhancement comes from the confinement of protein molecules in the nanoscopic cubic structure, which increases the chemical potential of protein fluid phase. As this effect is purely entropic, the method may be applied generally for various proteins. We have succeeded to explain our equilibrium phase diagram based on the idea of confinement. To establish the protein crystallization in the lipid cubic phase, however, the understanding of kinetics is also crucial. Because of the complex structure of cubic phase, protein molecules are expected to behave very differently from those in bulk solutions. In this study, we will use Fluorescence Correlation Spectroscopy (FCS) we have so far developed to monitor the diffusion process of protein molecules in the cubic phase. Protein solutions in the cubic phase have been found to exhibit a variety of 'nonequilibrium phases' such as liquid-like droplets and star-shaped aggregates. Since FCS detects the number fluctuation of protein molecules in a very small volume (less than 1 femtolitre), it can trance the local dynamics and is suitable for the study of microscopically phase-separated systems.