Even for such simple mixtures as (argon+methane), the excess enthalpy H-m(E) and the excess volume V-m(E) in the near critical region are about two orders of magnitude higher than for the liquid mixture at low temperatures and pressures near ambient conditions. Mixtures for which the critical temperatures are close together, and for which the critical pressures are far apart, have similar H-m(E) (x,p,T) and V-m(E) (x,p,T) surfaces, and near critical isotherms show double maxima in the supercritical fluid region. Mixtures for which the critical pressures are close together, and the critical temperatures are far apart, also have similar H-m(E) (x,p,T) and V-m(E) (x,p,T) surfaces, but isobars on the surfaces are ’S’ shaped. The shapes of these near-critical excess-function surfaces can be understood from an inspection of the enthalpy, or residual enthalpy curves of the mixture and of the pure components. Examples of both are given. Attention is drawn to the large value that these excess functions can have close to a pure component critical point.