A physical system is in local equilibrium if it cannot be distinguished from a global equilibrium by ``infinitesimally localized measurements''. This should be a natural characterization of local equilibrium, but the problem is to give a precise meaning to the qualitative phrase ``infinitesimally localized measurements''. A solution is suggested in form of a Local Equilibrium Condition, which can be applied to linear relativistic quantum field theories but not directly to selfinteracting quantum fields. The concept of local temperature resulting from LEC is compared to an old approach to local temperature based on the principle of maximal entropy. It is shown that the principle of maximal entropy does not always lead to physical states if it is applied to relativistic quantum field theories.