It is shown how to add dissipation to the resonant nonlinear oscillators studied by Ford and Lunsford in such a way that the system remains on the energy surface. In the dissipative system, the energy surface is stable in some directions and neutrally stable in other directions. The dissipative oscillators are special cases of the general type investigated by Sherman and McLaughlin. The connection between resonant conservative nonlinear oscillators and dissipative oscillators may make it easier to extend the theorem of Arnol'd to dissipative systems.