A self‐consistent thermodynamics is developed for nonrelaxation hysteretic processes. This theory, nonequilibrium thermostatics, is based upon macroscopic empirical descriptions of hysteretic behavior and the laws of thermodynamics. It is shown that the empirical behavior of hysteretic systems does not satisfy the conditions required for application of either equilibrium or relaxation nonequilibrium thermodynamics. Therefore, modified thermodynamic assumptions are proposed which are consistent with empirical hysteretic behavior. The principal new assumptions are (1) that processes (energy dissipation permitted) consists of a differential sequence of nonequilibrium states; (2) that three new ‘‘state variables’’ describe all of the ‘‘history dependence of a state;’’ (3) that at least some ‘‘reversible’’ processes exist; (4) that the time‐independent ‘‘modified Gibbs relation’’ can be used to describe the Second Law constraints. With these assumptions, it is shown that the thermodynamic relationships derived from the First Law are identical to those for standard equilibrium thermodynamics, but Second Law implications are significantly different, e.g., a new ‘‘dissipation’’ state function is derived; it is proven that hysteretic behavior is a positive indication of a dissipative process and that dissipation always causes hysteresis. It is concluded that nonequilibrium thermostatics provides a self‐consistent theory which extends the useful domain of thermodynamics to include nonrelaxation, hysteretic (dissipative)processes. A comparison of detailed predictions and experimental measurements of heat capacities, adiabatic paths, etc., for a hysteretic system is provided in a separate paper.