Free energy changes (DeltaG(degrees)(N-->D)) obtained by denaturant-induced unfolding using the linear extrapolation method (LEM) are presumed to reflect the stability differences between native (N) and denatured (D) species in the absence of denaturant. It has been shown that with urea and guanidine hydrochloride (GdnHCl) some proteins exhibit denaturant-independent (DeltaG(degrees)(N-->D)). But with several other proteins urea and GdnHCl give different (DeltaG(degrees)(N-->D)) values for the same protein, meaning that the free energy difference between N and D is not the only contribution to one or both (DeltaG(degrees)(N-->D)) values. Using beta1, a mutant form of the protein G B1 domain, we show that both urea- and GdnHCl-induced denaturations are two-state and reversible but that the denaturants give different values for (DeltaG(degrees)(N-->D)). While spectral observables are sensitive to the shift between N and D states (between states effect), they are not sensitive to denaturant-induced changes that occur within the individual N and D states (within state effect). By contrast, nonspectral observables such as Stokes radius and thermodynamic observables such as proton uptake/release are often sensitive to both "between states" and "within state" effects. These observables, along with spectral measurements, provide descriptions of urea- and GdnHCl-induced denaturation of beta1. Our results suggest that in the predenaturation concentration range GdnHCl changes the free energy of the native ensemble in a nonlinear manner but that urea does not. As with RNase A and beta-lactoglobulin, beta1 exhibits variable two-state behavior with GdnHCl-induced denaturation in that the free energy of the native ensemble in the predenaturation zone changes (varies) with GdnHCl concentration in a nonlinear manner.