A kind of linear nonequilibrium thermodynamieal system is reckoned as har-monic mapping.We generalized the Onsager coefficients from constants to func-tions of state variables

and applied harmonic mapping to deal with the steadstate and stability of stead state in system.By means

of harmonic mapping theory

we give out the criterion for judging the stability of stead state and discuss therelation between these results and the minimum entropy production theorem.