Information is presented about the spectral and other properties of Jacobian matrices occurring in the numerical solution of a number of large, very stiff ODE problems, arising from mass action kinetics. These properties demonstrate that the concept of a few “stiff” eigenvalues, the rest being “non-stiff”, is not valid for such problems; consequently, it is argued that partitioning and exponential-fitting methods are inappropriate for use in general-purpose software for stiff systems. Moreover, second-derivative methods and all but a very few formulations of implicit Runge-Kutta methods would be at a grave disadvantage when applied to large, very stiff problems.