A systematic development is given of the view that in the case of systems with long-range forces and which are therefore nonextensive (in some sense) some thermodynamic results do not hold. Among these is the relation U - TS + pΝ = Μ N and the Gibbs-Duhem equation. If a search for an equilibrium state is made by maximization of the entropy one may obtain misleading results because superadditivity may be violated. The considerations are worked out for a simple gas model, but they are relevant to black hole thermodynamics. Rather general conclusions can be drawn which transcend special systems.