A generalized thermodynamic description of one-variable complex chemical systems is suggested On the basis of the Ross, Hunt, and Hunt (RHH) theory of nonequilibrium processes. Starting from the stationary solution of a chemical Master Equation, two complimentary, related sets of generalized state functions are introduced. The first set of functions is derived from a generalized free energy F-X, and is used to compute the moments of stationary and non-Gaussian concentration fluctuations. Exact expressions for the cumulants of concentration are derived; a connection is made between the cumulants and the fluctuation-dissipation relations of the RHH theory. The second set of functions is derived from an excess free energy phi(x); it is used to express the conditions of existence and stability of nonequilibrium steady states. Although mathematically distinct, the formalisms based on the F-X and phi(x) functions are physically equivalent : both lead to the same type of differential expressions and to similar-global equations. A comparison is made between the RHH and Keizer’s theory of nonequilibrium processes. : An appropriate choice of the integration constants occurring in Keizer’s theory is made for one-variable systems. The main differences between the two theories are : the constraints for the two theories are different; the stochastic and thermodynamic descriptions are global in RHH, were Keizer’s theory is local. However, both theories share some common features. Keizer’s fluctuation-dissipation relation can be recovered by using the RHH approach; it is valid even if the fluctuations are nonlinear. If the thermodynamic constraints are the same, then Keizer’s theory is a first-order approximation of RHH; this approximation corresponds to a Gaussian description of the probability of concentration fluctuations. Keizer’s theory is a good approximation of RHH in the vicinity of a stable steady state : near a steady state the thermodynamic functions of the two theories are almost identical; the chemical potential in the stationary state is of the equilibrium form in both theories. Keizer’s theory gives a very good estimate of the absolute values of the peaks of the stationary probability density of RHH theory, Away from steady states the predictions of the two theories are different; the differences do not vanish in the thermodyn;amic limit. The shapes of the tails of the stationary probability distributions are different; and hence the predictions concerning the relative stability are different for the two theories.