We have studied the denaturation of metmyoglobin at pH 6.0 and 25 degrees C by urea and guanidine hydrochloride (GdnHCl) which are known to unfold the protein to the same extent. It has been observed that estimates of protein stability (Delta G(N-U)(0)) from urea-induced and GdnHCl-induced denaturations do not agree with one another; the linear extrapolation method gave Delta G(N-U)(0) values of 7.59 +/- 0.33 and 5.35 +/- 0.10 kcal mol(-1) for urea and GdnHCl denaturations, respectively. Measurements of the effect of the addition of KCl in the concentration range 0.1-1.0 M to urea denaturation have suggested that this disagreement is not due to the nonionic and ionic characters of urea and GdnHCl, respectively. The functional dependence of the free energy change of unfolding (Delta G(N-U)) on [denaturant], the molar concentration of the denaturant, has been investigated for understanding the cause(s) of the disagreement between the two estimates of Delta G(N-U)(0) of metmyoglobin. For this purpose, we have studied the GdnHCl-induced denaturation of the protein in the presence of different urea concentrations at pH 6.0 and 25 degrees C and vice versa. These measurements yield Delta G(N-U) values in the full concentration range [Ahmad et al. (1994) J. Biochem. 115, 322-327], and these results provide strong evidence that the Delta G(N-U) dependence on [urea] is linear (linear free energy model of denaturation) and the relation between Delta G(N-U) and [GdnHCl] is curved (binding model of denaturation). It has been observed that the extrapolated value of Delta G(N-U) in urea using the linear free energy model becomes identical to the extrapolated value of Delta G(N-U) in GdnHCl using the binding model.