Experimental temperature and density profiles are consistent with the assumption that they relax towards profiles related by T(x)/T0=(n(x)/n0)gamma -1 exp( alpha (1-(n0/n(x)))) (1), gamma =5/3=adiabatic constant, alpha >or=-( gamma -1)nmin/n0 independent of x; in most cases one has nmin=0. Cases of incomplete relaxation are exceptions, e.g. certain Tokamak discharges with pellet injection in which the temperature profiles are too flat compared with the corresponding density profiles. Relation (1) follows from the entropy principle proposed. According to it, Tokamak plasmas should relax towards states described by relations T=T(n(x)), in which the total entropy of the plasma does not change when the plasma performs arbitrary internal motions slow enough not to alter the relation between T and n. The relaxation is incomplete if it is too slow to compete with influences such as very strong local heating or very large local radiation. The profiles obtained by Biskamp (1986) and Kadomtsev (1986) from an energy principle assuming the electrical conductivity given by Spitzer's law sigma =const T(x)3/2 correspond approximately to alpha =1. To get agreement with the experimental profiles considered, however, alpha values ranging from 0 to 3 are required. Tokamak equilibria are usually describable in terms of two arbitrary functions of the poloidal flux psi . For resistive plasmas with Spitzer's formula valid one can choose the temperature and density as these function. Equation (1) reduces this freedom to the free choice of one function, say T( psi ), and of a special value of the parameter alpha . Examples are presented for cylindrical plasmas with circular cross-sections. A comparison with Coppi's temperature formula ('profile consistency', see Coppi, 1980) leads in many cases to very good agreement. Combining Coppi's formula with relation (1), one obtains density and temperature profiles depending only on the two quantities alpha and beta r2, with beta being related to the plasma radius and the safety factor. Examples of a few values are shown.