The glass stability (GS) parameters, recently introduced by Fan (Phi), Yuan (beta) and Long (omega), which are based upon the three characteristic temperatures: T-g-glass transition temperature, T-x-onset of the crystallization peak (or T-c-maximum of the crystallization peak), and T-m-melting temperature, are expressed in this paper via the ratios r = T-x/T-g and m = T-m/T-g. In an earlier paper, we applied the same procedure on the Hruby (K-H), Weinberg (K-W) and Lu-Liu (K-LL) parameters. Thus, the GS parameters are more directly related to the supercooled region and reduced glass transition temperature. The objective was to find out how these GS parameters are sensitive to the changes of r and m, and whether this is reflected on the correlation of the given parameter with the glass-forming ability (GFA). The theoretically derived relation d beta/dr > dK(H)/dr > dK(LL)/dr always holds, and d beta/dr > dK(H)/dr > d omega/dr > dK(LL)/dr is also probable, while the order of sensitivity to m is d beta/d(m) > d omega/dm > dK(LL)/dm. Testing on one series of oxide glasses and two series of bulk metallic glasses confirmed in full these relations. The parameter beta is the most sensitive to the changes of both r and m, while K-LL. is generally least sensitive. Partial sensitivity of a GS parameter to r and m is not related to the coefficient of correlation between the GS parameter and CFA, whereas the ratio dGS/dr : dGS/dm can explain the magnitude of the correlation coefficient. (C) 2010 Elsevier B.V. All rights reserved.