Windows 2003 in a Windows NT Domain

We're looking to upgrade a couple of our production servers to W2K3. The rest of our network is still running WinNT. We'd like to migrate our entire network slowly so we don't take down too many production servers at a time. Does anyone know of any incompatibilities with putting W2K3 member servers on a WinNT domain? These machines would, ideally, have trust relationships with each other. If that's not possible, then we'll probably have to create two separate networks (which I'd rather not do).