Among various non-linear regimes of electron cyclotron instabilities that may be driven by a strong electron cyclotron resonance (ECR) heating in open magnetic traps, the continuous generation of a quasi-monochromatic wave, characterized by a smooth release of a free energy from a system, is especially important for applications, e.g., aimed at performance optimization of ECR ion sources. We study an universal model based on the quasilinear description of plasma–wave interactions that explains the condition of a continuous-wave regime of the cyclotron instability observed experimentally including, in particular, a strong dependence on a magnetic configuration.