Plasma equilibrium with dissipation is governed by more equations than the one used for stability problems in ideal magnetohydrodynamics. Consequently, as transport processes became more important in fusion experiments, it is necessary to determine whether an equilibrium will eventually be reached after a long time at the end of the transport processes. A study is made of a cylindrical plasma with an ohmic heating current as an approximation to a large aspect‐ratio tokamak. For comparison, both single‐fluid theory and two‐fluid theory are used. It is found that no equilibrium exists in the single‐fluid theory with a plasma temperature dropping to zero at a finite radius, while such an equilibrium does exist in two‐fluid theory provided that the electron temperature is higher than twice the ion temperature. Both the low‐pressure and high‐pressure cases are studied in the tokamak parameter range. Analytical results for the plasma behavior near its edge are also obtained.