In this study, we present a generalized theoretical framework for fractional velocity particles (FVPs) in RF linacs. The framework describes a hierarchy of FVPs with 𝑣/𝑣_0=1/ℓ (ℓ = 2 , 3, 4, …) , and the underlying mechanism responsible for their long-term acceleration and momentum-halo formation is systematically elucidated. These particles are produced at the early stage of acceleration and continue to be accelerated by their own RF buckets (called the fractional RF buckets hereafter) along with the leading velocity particles that are captured by the leading RF bucket. This characteristic can be explained as a basic feature of a kind of nonlinear mapping describing the longitudinal beam dynamics of RF linacs without losing its essential properties. The stability of these halo particles in the transverse direction is analyzed assuming a typical solenoid guiding system. Some of the momentum halos are shown to survive for a long time in the beamline. These results strongly suggest the necessity of momentum collimators in lower-energy regions for extremely high-intensity linacs such as the IFMIF Demo Oriented NEutron Source (DONES) or a 1 A single-cell cavity linac for nuclear waste transmutation.