An ongoing question is whether the isokinetic, isoenergetic or other thermostat models are acceptable as model of thermostats in nonequilibrium statistical mechanics as opposed to thermostats which are made of infinite Hamiltonian systems in thermal equilibrium. I will discuss the problem and the strict equivalence of the isokinetic, isoenergetic and Hamiltonian thermostats in the thermodynamic limit and the difference between the 1,2 dimensional systems and the 3 dimensional (or higher) ones.