We relate the condition for the elliptic shape of the phase diagram of proteins to the degree of correlation in the fluctuations of the changes of enthalpy and volume at the denaturing-refolding transition. Since this degree cannot be larger than 1, hyperbolically shaped diagrams are not likely to exist. Experiments show that the correlation factor is actually quite low for proteins implying that one-order parameter is not enough to describe the folding-denaturing transition. These findings seem to be the thermodynamic manifestation of the glasslike properties of proteins despite the fact that the transition itself is of first order. (C) 2004 American Institute of Physics.