We present a Hamiltonian treatment of gyrotrons and cyclotron auto-resonance masers for the cases of resonant particle evolution in a constant electromagnetic field and also for when the field evolves self-consistently with a single resonant particle. The former case relates to high-Q cyclotron resonance maser (CRM) oscillators operating close to saturation or to low-gain devices, whereas the latter describes the self-consistent CRM evolution both of the field and of electrons when the electron beam is perfectly pre-bunched. The particle phase spaces are described in detail for both cases.