A con-current multiscale non-equilibrium molecular dynamics is proposed. The notion of multiscale canonical element ensemble is put forth, which enables us to employ the coarse grain field as a heat bath, and it is accomplished by using a distributed Nose-Hoover thermostat network. In doing so, it guarantees that the non-equilibrium molecular dynamics returns to a canonical equilibrium state when external disturbances vanish, which may have not been the case for the non-equilibrium molecular dynamics in the literature. We have shown that the non-equilibrium distribution function is canonical. (C) 2007 Elsevier B.V. All rights reserved.