We point out a set of generalized state equations $p = \psi(\rho,A)$ requiring the full exceptionality of the M.F.D. system for a one-dimensional flow. Precisely we find that the $\psi(\rho,A)$ functions must satisfy a second order parabolic equation; so we are able to determine a set of solutions expressed by means of two arbitrary functions depending on the Riemann invariant $A/\rho^{2}$.