Stability limits for different energy truncated models of quasi-isothermal cores of globular clusters are defined and calculated by a method that does not make use of more than equilibrium configurations. All models of isolated clusters, including isothermal spheres, become unstable when the ratio v(escape)/v(dispersion) is not less than 4 at the center. The limits of appropriate models are well correlated with the changes in the evolution observed by Spitzer et al. in calculated collapsing cores. Most observed globular clusters, whose parameters allow calculation, are close to marginal stability.